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WHY THERE I S SOMETHI NG RATHER THAN NOTHI NG 105
We have already criticized Descartes’s Cogito, sum and
Heidegger’s existentialist phenomenology of Da-sein or human
being-in-the-world as inadequate methods of pure philosophical
ontology. We withhold discussion until later of the Big Bang, God’s
decision to actualize the world, and the 50–50 random logical prob-
ability of the existence rather than nonexistence of an actual world.
As explanations of why there exists something rather than nothing,
we shall see that these alternative proposals in one way or another are
explanatorily inadequate. Thus, we are left with only the combinato-
rial theory.
Combinatorial answer to the question of being
We have asked: what makes an object as a mere subject of predication
existent or nonexistent? What makes a state of affairs existent or
nonexistent? What makes a logically possible world existent or non-
existent? The answers, we have argued, must all depend on the same
logical foundation in a combinatorial pure philosophical ontology.
When we spin out all the combinations of all the logically possible
predication objects with all the logically possible properties, we can be
sure that there must be at least one maximally consistent combination.
That combination, or combinations if there is more than one, on the
present definition, satisfy the requirements for actual existence, or,
more simply, are actual, real, exist or have being. Mere logically possi-
ble worlds, mere logically possible states of affairs, and mere logically
possible objects, are not actual or real, and do not exist or have being,
in the real world or in any non-actual merely logically possible world.
As mere possibilia, they are sure to be internally predicationally consist-
ent but submaximal. We have argued that, contrary to conventional
modal semantics, we can and should interpret non-actual merely
logically possible worlds as at most submaximally consistent. Non-
existent worlds, nonexistent states of affairs and nonexistent objects
must therefore be missing something that real entities have. On the
present account, they do not lack Dasein or das Modalmoment or
Plato’s special Form of Being; they fail to exist because they are either
predicationally inconsistent or submaximal.
Why is there something rather than nothing? We have argued that
an actual world is logically necessitated; it is logically combinatorially
necessary that something rather than nothing exist, given the defini-
tion of being as maximal consistency. The actual world is a maximally
consistent states-of-affairs combination; and we know, logically, since
there is no contradiction in the concept, without consulting any data
106 ONTOLOGY
of the actual world or our experience or phenomenological analysis
of our experience of it, that there exists at least one maximally
consistent combinatorial possibility of objects with properties. Logi-
cally, therefore, there must exist a world; the existence of an actual
world is logically combinatorially necessary.
Again, this answer to the question of being concerns the meaning of
the concept of being, of what it means for something to exist. We as-
sume that pure philosophical ontology is only a discipline, and cannot
be construed as a domain, and that since logic is also a discipline, there
is no special logical or metaphysical reason why pure logic as opposed
to phenomenology or some other discipline could not be invoked to
answer the question of being or the fundamental problem of metaphys-
ics. The thesis that to be is to be maximally consistent offers a unified
account of the meaning of existence assertions for any existents, since
the reduction of ontology to logic is conducted entirely in terms of
logically possible objects and logically possible properties. We do not
suppose that pure logic can be used to deduce the content of an ontol-
ogy in the sense of uniquely specifying a preferred existence domain,
either in theory or as the extant domain of real existents.
Nor have we tied our hands in other ways with respect to the deliv-
erances of applied scientific ontology. We have not tried to say what
kinds of things objects and properties are, whether one is reducible to
the other or not, whether properties are just a special kind of object or
objects are constituted by and in that sense reducible to property com-
binations. For the purposes of combinatorial ontology it has not really
mattered, because the objects are only logical, considered to be merely
logically possible predication subjects. We explain why there exists
something rather than nothing as a logical necessity. It is logically
necessary that something exist rather than nothing, but we have not
excluded the further conclusion that the actual world is logically
contingent, or that the actual world as one particular logically possi-
ble world happens to exist.
Something rather than nothing exists because “something” is a
logically general way of designating an actual world that is not neces-
sarily the actual world in all its particularity. It by no means follows
that human beings with their grabby Da-seins exist to experience the
actual world, whatever character it chances to have. The possibilities
inherent in pure logic offer a less anthropocentric way of understand-
ing the question of being in a combinatorial ontology than phenom-
enology does in Heidegger’s existentialist ontology, with its emphasis
on the concept of specifically human being-in-the-world. There is
something rather than nothing because:
WHY THERE I S SOMETHI NG RATHER THAN NOTHI NG 107
1. To be means to be maximally consistent, which is a purely logical
qualification, whether we are speaking of the being or existence
of an individual object, a state of affairs or an entire actual world,
including the actual world in all its particularity.
2. We know combinatorially that there is certain to be at least one
maximally consistent states-of-affairs or object–property combi-
nation that constitutes and is linguistically representable as an
actual world, a world all of whose states of affairs actually exist,
involving all and only actually existent objects. There must be
such a combination because there is no contradiction in the idea
of there being such a combination.
It is from the logical possibilities for combinations of properties,
the distribution of all logically possible properties over all logically
possible objects understood as logical predication subjects, that we
deduce the logical necessity of the existence of an actual world. There
must be a maximally consistent logically possible combination of just
the properties that constitute a world of maximally consistent actual
objects in maximally consistent actual states of affairs. What it is to be
(existence sense) is therefore in a sense to be (predication sense) one
of these so-defined actual entities, one of these so-defined actual
states of affairs or the so-defined actual world.
The analysis of being as maximal consistency applies at each level
of the combinatorial ontology. An actual object is a maximally consist-
ent property combination; an actual state of affairs is the possession
by any actual entity or entities of any of the properties in their respec-
tive maximally consistent property combinations. An actual world is a
maximally consistent combination of actual states of affairs. The
actual world is a particular maximally consistent combination of
actual states of affairs. From the fact that all actual states of affairs and
all actually existent entities can belong at most only to one truly
maximally consistent states-of-affairs combination, it follows as a
further implication that there uniquely exists only and at most one
actual world, so that, as we shall see, an actual world must be identical
with the actual world. To be is to belong to one of these three kinds of
entities – existent objects, actual states of affairs or an actual world in
its entirety – and hence, ultimately, of logically possible predication
objects having predicationally maximally consistent logically possible
property combinations.
Logically, there must be just one combination of properties to
objects that exactly instantiates the entities and states of affairs that
constitute the actual world. In the distribution of all logically possible
108 ONTOLOGY
properties over all logically possible predication objects, there is
certain to be at least one maximally consistent combination. Should
we call such a combination, or combinations, if there are more than
one, an actual world or the actual world or actual worlds? The
question is cantilevered. If we are satisfied with the explanation of
why there exists something rather than nothing, which the concept
affords, then we may also be inclined to accept the definition. The
trouble is that we are not yet in a secure position to judge whether the
explanation is satisfactory. We can probably agree, no matter what
view we take with respect to the relation between logic and ontology,
that the explanation is unacceptable if it does not support a further
argument to show that there can at most exist one actual world, that
it is identical to the world we happen to inhabit, and that the actual
world is logically contingent. That is the subject to which we turn
next.
Why there is only one logically
4 contingent actual world
Actual existence
It is reassuring to know, in the progress we have made so far, that
there must exist something rather than nothing. The two outstanding
problems left to be solved in pure philosophical ontology, concerning
the uniqueness and logical contingency of the actual world, must also
be addressed before we can be said to have satisfactorily answered the
question of being.
If we try to answer the question why there exists something rather
than nothing combinatorially, by arguing that an actual world must
exist, then we leave open at least temporarily the question whether only
one actual world exists. We do not commit ourselves thereby to a logi-
cal and ontological relation holding between the necessary existence of
an actual world and the presumably logically contingent existence of
the actual world. Nor have we said enough yet to relate the existence
of the actual world and the existence of an actual world by whose
necessary existence we answer the question why there exists something
rather than nothing. If it is logically combinatorially necessary that all
logically possible combinations of all logically possible states of affairs
include at least one maximally consistent combination, then it remains
at least conceivable that there be more than one maximally consistent
combination, of which the actual world that we know through experi-
ence might be only one among many distinct actually existent actual
worlds. Can we make sense of any of these consequences?
We must satisfy ourselves that the actual world is uniquely existent,
that an actual world can only be the actual world, and that the actual
world is logically contingent. If we cannot establish these two further
conclusions, then we must reconsider the wisdom of accepting Princi-
ple 3 with its implications for the question of being and the question
of why there exists something rather than nothing.
110 ONTOLOGY
The first problem concerns the presumed unique existence of the
actual world. Why should there be only one maximally consistent
combination of states of affairs or of objects with properties? Why are
there not distinct multiple realities or actual worlds, each of which,
according to the definition in Principle 3, actually exists? The
argument we have already presented for the reform of the conven-
tional semantics of modal logic implies that non-actual merely
logically possible worlds are at most submaximally consistent. What
we have not yet tried to show is that there is or can be only one
maximally consistent states-of-affairs combination corresponding to
the one and only actual world. Why, if in fact it is true, are there not
many actual worlds, many actualities, just as there are many planets
and galaxies within the actual world, of which we happen to inhabit
only one? Why should we not suppose that there are parallel simulta-
neously existent alternative universes?
The second challenge is to reconcile the logical necessity whereby
an actual world must exist with the assumption that the actual world
is logically contingent. An actual world, construed as a maximally
consistent states-of-affairs combination, exists as a logical necessity.
There must be at least one such combination among the totality of all
logically possible combinations. It is, therefore, logically necessary, an
inescapable consequence dictated by the requirements of pure logic,
that an actual world exists. Thus, we know why there exists some-
thing rather than nothing. The particular world that actually exists,
and, indeed, any actually existent logically possible world, is never-
theless presumably logically contingent in the sense that another
world logically might have existed instead and any of the physical
states of affairs that constitute the actual world logically might have
been otherwise than they happen to be.
What does this mean, and how, if at all, can we account for the
unique existence and logical contingency of the actual world within
the framework of a combinatory pure philosophical ontology? We
first address the uniqueness of the actual world and then the question
of its logical contingency.
An actual world = the actual world
What is the relation between the existence of an actual world where
something (or other) must exist, and the existence of the actual world
that we thinkers inhabit? We shall see that they are identical, and that
logic proves the existence of the actual world when it proves the exist-
ence of an actual world. There can exist only one actual world, as we
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 111
have interpreted the concept, because logically there can exist only
one maximally consistent states-of-affairs combination.
The argument relies on the fully explicated meaning of the
predicational completeness of an existent entity defined in terms of its
maximally consistent property combination. Thus far, we have held
only that there exists at least one maximally consistent states-of-affairs
combination. This is enough, in conjunction with Principle 3’s defini-
tion of an actual world, to establish that there exists at least one actual
world – that something rather than nothing exists. We are strongly
predisposed to believe, it may be unnecessary to say, that there is and can
be only one actual world, and that this implication is somehow neces-
sitated by the concept of an actual world. The problem is how we are
to prove that the actual world is uniquely existent. Is there a combina-
torial justification for the proposition that there can be at most one
actual world?
The proposed reform of modal semantics implies that all logically
possible worlds other than the actual world are predicationally
incomplete and hence non-actual, nonexistent. The difficulty is
explaining why merely logically possible worlds are non-actual. The
thesis follows immediately from our revised modal semantics, in which
an actual world is distinguished as a maximally consistent states-of-
affairs combination, and in which every non-actual merely logically pos-
sible world has predicational gaps – at best a submaximally consistent
states-of-affairs combination. The following inference summarizes this
line of reasoning, in which the crucial assumption is that on logical
grounds there can exist only one maximally consistent states-of-affairs
combination. The argument states:
Unique existence of the actual world
1. An actual world exists.
2. An actual world is a maximally consistent states-of-affairs
combination.
3. There can exist only one maximally consistent states-of-affairs
combination.
4. An existent actual world = the actual world.
The analysis depends heavily on assumption 3. Why suppose that
there can be at most one maximally consistent states-of-affairs combi-
nation? There exist multiple existent objects and multiple existent
states of affairs, all of which are supposed to be maximally consistent
of their kind. Why, then, suppose that there exists exactly one actual
112 ONTOLOGY
world rather than many actual worlds, each of which in different ways
is also maximally consistent? Is there something about the concept of
maximal consistency that precludes a multiplicity of maximally
consistent states-of-affairs combinations, of actual worlds, but
encourages the multiplicity of particular existent objects and states of
affairs? If the actual world is logically combinatorially identical with
an actual world logically necessitated by the logical possibility of that
combination of states of affairs, then does not the actual world with
all its states of affairs, objects and properties, share equally in the
logical combinatorial necessity by which we propose to explain why
there exists something rather than nothing?
Ontology of the actual world
So quickly do we go from logical rags to an embarrassment of appar-
ently excessive ontological riches in pure philosophical ontology. The
very idea of actual worlds other than the one we inhabit seems
confused. But how, precisely? What does a combinatorial answer to the
question of being imply about the unique existence of the actual world?
We should not consider the combinatorial pure philosophical
ontology outlined in Principles 1–4 to be correct unless we can argue
convincingly that there is only one actual world, unique in its actuality.
This is what we expect any competent pure philosophical ontology to
conclude. It is only a question of whether a good answer can be given
from the resources of pure logic, or whether we must turn to another
more opulent discipline like phenomenology in order to answer the
question of being. We make a case here for a purely logical justification
of the uniqueness of the actual world from the standpoint of combina-
torial pure philosophical ontology, arguing that logically there can at
most exist only one maximally consistent states-of-affairs combination.
We can, and probably should, continue to remain neutral about the
existence of abstract entities until we are ready to take on applied
scientific ontology with a better idea of what we mean when we ask
whether this or that putative entity actually exists. The dilemma we
have already considered is that abstract objects either do not exist at
all, or, if they do exist, exist alike in every logically possible world,
including non-actual merely logically possible worlds. If we leave
abstract entities out of account, on the strength of the dilemma, then
we are left to contemplate only physical states of affairs involving
physical entities, objects and events in real time, that by their
differences distinguish one logically possible world from another. The
actual world is, of course, a logically possible world; it is just not
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 113
merely logically possible, but something more. If we do not want to
say that it is something more because it also has Dasein or das
Modalmoment of full-strength actuality, or Being blended in with the
other Forms of its objects, then we might find it best to say that it does
not need to be anything more, but exists or has being by virtue of a
property of its distinguishing states-of-affairs combination considered
as a whole, such as the property of being maximally consistent.
Thus, we ask again, is the actual world unique, or might there exist
other actual worlds? Is it a consequence of the definition of an actual
world as a maximally consistent states-of-affairs combination that
there can be only one actual world, the actual world, and therefore
the world we inhabit? Or, could (and therefore must) there be,
according to the proposed analysis, multiple maximally consistent
states-of-affairs combinations or multiple maximally consistent
object–property combinations? If these are permitted, which is to say
necessitated, by the analysis, then it casts the definition of being as
maximal consistency in a bad light. We are no better off than conven-
tional modal semantics in that case, because we are no better able to
distinguish the existent actual world that we inhabit from other non-
existent merely possible actual worlds than by referring to our empiri-
cal experience or phenomenology of human being-in-the-world, or
staking out ontological territory indexically, declaring this to be the
actual world, the one and none other that we experience and ostend
and feel its comforting or terrifying resistance.
The reason why there is exactly one actual world rather than a
multitude of existing actual worlds has nothing to do with the fact
that we cannot imagine or would be unable even in principle to
experience multiple actual worlds. There appears to be something
logically or conceptually necessary about there existing only one
actual world; that to speak of the actual world, no matter how or by
what states of affairs it is constituted, is to speak of a uniquely existent
thing, the existence of the universe in the sense of a closed single
unitary realm of all being. If that is the correct concept, we must
continue to ask, how can it be proved? The combinatorial pure philo-
sophical ontology that we have developed implies, with the help of
pure logic, that there cannot be more than one actual world.
If there were two or more actual worlds, then there would be two or
more maximally consistent states-of-affairs combinations. The actual
world as a maximally consistent states-of-affairs combination is ulti-
mately constituted out of all logically possible combinations of all logi-
cally possible objects and all logically possible properties. Logically,
then, there can be no additional logically possible objects with which to
114 ONTOLOGY
determine another numerically distinct alternative actual world. The
actual world as a maximally consistent states-of-affairs combination
ontologically underwrites all true propositions. The existent objects in
one actual world per impossibile would then need to be so related to all
existent objects in an alter actual world that they logically coalesce into
a single unified actual world, like two beads of mercury touching. Only
such a unified uniquely existent actual world is maximally consistent.
If both actual world A and actual world alter-A coexist, then their con-
stitutive states of affairs must be jointly logically consistent, and so they
must both belong to and only to a maximally consistent states-of-affairs
combination. It follows, then, that A and alter-A can only be two names
for the same logically possible world that is actual on the present
account by virtue of being maximally consistent.
By this reasoning we justify the common-sense conclusion that there
can exist only one actual world. The argument strongly depends on the
assumption that there can at most exist only one maximally consistent
states-of-affairs combination, but does not preclude the existence of
many objects and many states of affairs. We have argued that the
concept of maximal consistency literally applied entails that there can
exist only one maximally consistent state of affairs combination. Its
predicational maximality makes every other states-of-affairs combina-
tion predicationally incomplete, and hence by definition nonexistent,
non-actual. If we are truly to have a logically possible maximally con-
sistent states-of-affairs combination, it must, by virtue of its maximality,
already include in its combination any existent entity, including such
large-scale hypothetical entities as additional maximally consistent
states-of-affairs combinations. All hypothetically maximally consistent
states-of-affairs combinations therefore logically coalesce into one.
According to the combinatorial concept of being, there can exist at most
only one actual world. We can rest assured that logically not only must
there be something rather than nothing, but that there is only one actual
world. The universe, as the name implies, is one.
None of this is to deny the logical possibility of widely separated
“universes” within a single actual world. These would have to be
distinct “worlds” in the sense of vastly separated distinct spacetime
regions between which there are no causally possible interrelations or
intercommunication beyond what any epistemic agents might mistak-
enly believe to be the limits of the actual world. We have said nothing
whatsoever yet about the applied scientific ontology of space or time
or spacetime, whether or not there can be spacetime islands that are
totally physically isolated from one another, what the capabilities and
limitations of epistemic agents might be, or any of the other specific
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 115
applied ontological details we would need from a metaphysical stand-
point even to begin deciding whether such possibilities ought to be
considered. If there are spacetime islands, and we are stranded on
one, we could presumably never know it from a practical epistemic
standpoint. A combinatorial pure philosophical ontology does not
preclude such a possibility, which does not contradict the unique
existence of the actual world considered as a whole, even if it happens
to include physically insular spacetime regions.
By regarding only the actual world as maximally consistent, we
avoid the schizophrenia that attends conventional modal semantic
explanations of the ontological status of non-actual merely logically
possible worlds. These are supposed to exist as abstract entities
because they are defined as abstract sets of abstract propositions, on
the realist assumption common in formal symbolic logic and math-
ematics that abstract mathematical entities necessarily exist. Non-
actual merely logically possible worlds exist (as abstract entities) on
this account, even though they do not exist (as actual or actualized, or
are not identical with the actual world). The combinatorial analysis of
the concept of being on the contrary entails that non-actual merely
logically possible worlds do not exist in any sense, even as abstract
entities, because they are at best submaximally consistent. Other
worlds are logically possible only in the sense that, had the facts of the
actual world been different, they logically could have existed, in that
no logical contradiction results in supposing that they rather than the
actual world could instead have turned out to constitute the one and
only maximally consistent states-of-affairs combination.
Physical states of affairs
We have already mentioned the need to introduce physical states of
affairs as a subcategory in pure philosophical ontology. We must do so
if we are to make sense of distinctions between logically possible
worlds that cannot be understood in terms of nonexistent or
uniformly existent abstract states of affairs alone. It might seem
impermissible to draw conclusions about the existence of physical
entities from within the project of pure philosophical ontology. The
conclusion is nevertheless a necessary consequence of the identity
conditions for distinct logically possible worlds.
Physical states are a logical possibility; thus, there is a combination
of logically possible physical states that exactly describes the actual
world. The argument can also be recast in terms of the difference
between spatiotemporal and non-spatiotemporal properties. Assume,
116 ONTOLOGY
as an instance of excluded middle, that all properties of all predicables
are either spatiotemporal (physical) or non-spatiotemporal (abstract).
If all properties are non-spatiotemporal, then all identically belong to
all logically possible worlds, actual or non-actual. In that case, there is
no way to distinguish any logically possible world from any other,
since all have precisely the same complement of abstract properties,
constituting one and the same logically indistinguishable maximally
consistent states-of-affairs combination, involving only the properties
of abstract non-spatiotemporal properties, which do not vary from
world to world. All worlds then collapse into one, and all truths turn
out to be logically necessary. The actual world, indistinguishable from
logically possible worlds generally, would then be logically necessary.
The explanation of why there exists something rather than nothing
is easily answered if there are only abstract entities. It is necessarily
true that something rather than nothing exists on the present assump-
tion, because the actual world as the only logically possible world
necessarily exists. The answer is disappointing, because it amounts to
saying that something rather than nothing exists because the only
existents are abstract entities that cannot fail to exist in any logically
possible world. The conclusion is further at variance with empirical
evidence about the nature of the actual world, however reluctant we
may be to include experiential facts about the logically contingent
nature of existence into the deliberations of pure philosophical ontol-
ogy. It is interesting to see that we nevertheless obtain the same
answer to the question of being by this route – that to exist is to be
maximally consistent.
If, on the other hand, there are differences between logically possi-
ble worlds, they cannot involve non-spatiotemporal entities, and
must therefore depend exclusively on differences among spatio-
temporal, which is to say physical, properties. The same answer to the
question of being is sustainable also on the assumption that there are
spatiotemporal or physical properties of objects. As a bonus, we
further conclude that there are spatiotemporal physical properties as
well as non-spatiotemporal abstract properties. We again leave aside
the question whether properties themselves are physical or abstract as
a topic for applied scientific ontology, and recognize that even here
the conclusion that there are spatiotemporal or physical properties is
only hypothetical, conditional on the assumption of only one horn of
a dilemma. It is heartening nonetheless to see that things can turn out
this way for applied scientific ontology as far as pure philosophical
ontology is concerned. The result reinforces previous arguments for
the submaximal consistency of non-actual merely logically possible
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 117
worlds. If we have reason later on to believe that there is only one
spacetime realm within which spatiotemporal properties can be
instantiated, then it follows that non-actual worlds are inherently
incomplete or submaximal with respect to all logically possible physi-
cal spatiotemporal properties, and hence non-actual.
We argue in what follows that the uniquely existent actual world is
logically contingent in all its physical states of affairs. The recognition
of physical states of affairs as a distinguished category of logically
possible states of affairs does not poach on applied ontology’s terri-
tory, because pure philosophical ontology must be as neutral about
the ontological status of physical states of affairs as it is generally
about the ontic status of any other subcategory of states of affairs. The
states of affairs in question are purely logical, as far as the argument at
this stage is concerned, in that they involve only the logically possible
combinations of logically possible objects and logically possible
properties, including logically possible physical objects with logically
possible physical properties. We consider the division between physi-
cal and abstract objects and properties as grounded on a more purely
logical distinction if we construe it as a division between spatio-
temporal and non-spatiotemporal objects and properties. We have
only ontological play-money to spend in pure philosophical ontology
anyway. We have argued that an actual world exists because logically
combinatorially there must be such a possibility that by definition
must exist. We have also maintained on the basis of the combinatorial
analysis of being that there can be only one uniquely existent actual
world, that the actual world is correctly so designated in the sense that
there can be only one, and that combinatorially the existence if not
the condition of the actual world is logically necessary.
Logical contingency of the actual world
If logically there must exist a world, and if the actual world exists,
then a careless inference might have it that therefore the actual world
with all its particular states of affairs logically must also exist. The
actual world, we would nevertheless like to believe, is logically
contingent in at least some of its states of affairs, and presumably in all
of its physical spatiotemporal states of affairs. If combinatorially there
must exist an actual world, how then are we to prove the logical
contingency of the actual world?
The problem we must now address is to account for the presumed
logical contingency of the actual world. When we ask, indicating the
surrounding actual world in which we find ourselves, why is there
118 ONTOLOGY
something rather than nothing, we do not usually mean the actual
world as it actually exists. The world could be very different than it is;
but a world of some kind with some physical states of affairs or other
would still exist.
The logical contingency of the actual world must be due to the fact
that it is partly constituted by spatiotemporal objects and states of
affairs existing in real spacetime. The events unfolding in the vast causal
spatiotemporal matrix include, but are by no means limited to, the tiny
part of the universe where we happen to dwell. This is a good non-
empirical reason for considering physical states of affairs in addition to
abstract objects as possible entities to be accommodated in a later
applied scientific ontology. The topic of the logical contingency of the
actual world is a delicate one in the context of the foregoing combina-
torial argument that there must and therefore does exist something
rather than nothing. If the existence of an actual world is logically
necessary, how can the details of the actual world, its facts and events
and occurrences, the condition as well as the existence of the actual
world, be merely logically contingent? How, in particular, can the actual
world be logically contingent if the existence of an actual world is
logically combinatorially necessary, and if there is only one uniquely
existent actual world, if an actual world = the actual world?
It is deductively invalid to infer a proposition with more informa-
tion content than the inference’s assumptions. If we are required by
the logical analysis of being as maximal consistency to admit that all
the states of affairs of the actual world are logically necessary rather
than logically contingent, then we either owe an explanation of how
we can survive deductive invalidity in proving the logical contingency
of the actual world in pure philosophical ontology, or we must
consider withdrawing the analysis.
We have not tried to prove the actual existence of any logically
contingent physical spatiotemporal entities, and we have certainly not
done so from the standpoint of pure logic. Any such attempt would
evidently be deductively invalid. Instead, we have proceeded condi-
tionally. If there are physical spatiotemporal entities, we have said, then
at least whatever complex physical spatiotemporal entities exist are
combinatorially guaranteed to vary from logically possible world to
logically possible world. Each world, indeed, will comprise and consist
of a distinct such combination. This is logically all we need in order to
satisfy ourselves that if physical states of affairs enter into the consti-
tution of the actual world, then those states, since they characterize at
most some but not all logically possible worlds, as the concept is
defined, are logically contingent. By implication, if physical states of
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 119
affairs enter into the constitution of the actual world, then the condi-
tion of the actual world is not logically necessary but contingent.
As preparation for an explanation of the actual world’s logical
contingency, we examine two different accounts of the actual world’s
unique existence and logical contingency. One, like Leibniz’s meta-
physics, invokes the existence and free choice of God to actualize a
world from a range of alternative logical possibilities, and the other
postulates the Big Bang of physical cosmology to explain the existence
and logical contingency of the entire physical universe. The criticisms
offered here apply with equal force to the idea that God’s choice or
the Big Bang might explain, in response to our previous question, why
there exists something rather than nothing. Throughout, we refer to
the logical contingency of the actual world’s physical states of affairs
or to the actual world considered from the standpoint of its physical
states of affairs. We thereby bracket the ontic status of abstract
objects, and remain ontically neutral about their existence or non-
existence until we are ready to recommend a particular preferred
existence domain in applied scientific ontology.
God’s choice of a world to actualize
We first briefly consider the idea that God chooses a particular world
to actualize. Methodologically, we cannot invoke a particular existent
entity whose contested existence is recognized only by some applied
ontologies as belonging to some but not all theoretical preferred exist-
ence domains. If the logical contingency of the actual world is to be
explained as a question for pure philosophical ontology, then we
cannot appeal even heuristically to the existence of God or God’s
choice at any point without plunging into another form of
Heidegger’s circle.
Nor does it help to appeal to God’s perfect good will in choosing to
actualize a particular world, as Leibniz does in his theomodal theory,
“On the Ultimate Origination of Things”. Leibniz holds that the exist-
ence of the actual world in its actual condition is the result of God’s
choosing to actualize this particular world from among all logical pos-
sibilities. Why an infinitely perfect being should need to go through
any sort of process or procedure of projecting and selecting in order to
create the world is already puzzling. If we ignore the most obvious
embarrassing questions, and think about the choice of one among an
array of alternative logically possible worlds as a model or metaphor
for the uniqueness and contingency of the actual world, then we
are sure to be disappointed. We first need a sound theological or
120 ONTOLOGY
philosophical reason for agreeing that God’s perfect infinite good will
does not require God on the contrary to actualize multiple actual
worlds, none of which is the best, but each of which is qualitatively an
exact equal among the best of all logically possible worlds. Why
suppose without good argument that there is a single best logically pos-
sible world? We similarly need a good reason for admitting that God’s
perfection does not in the end require actualizing a world in which no
events are logically contingent. God might, as Leibniz pictures him,
array before divine imagination all the alternative logically possible
worlds, in order to consider which is or are best, until, as part of the
divine decision process, God sees all possibilities dramatically collapse
into one, which, by virtue of its overriding logical necessity, there being
no other genuine possibilities left, awaits only God’s decision about
whether or not to actualize any world at all.
1
For the same reasons it does not help to refer to the existence of
God as choosing existence over nonexistence for an actual world or
for the actual world in its existent state. Are we sufficiently desperate
to argue that it is a consequence of God’s perfection that God must
actualize some world or other, and that the actual world is de facto
whatever world God chooses to actualize? God’s choice is no philo-
sophical help in trying to understand why the actual world exists.
Aside from the dubious picture of God entertaining ideas and making
decisions in real time, the existence of which apparently is dispensable
as merely heuristic or else requires no explanation, there is also the
philosophically questionable existence of God as a suitable starting
place for trying to answer the question of being. We would not be the
first to advance the dilemma that, if existence is supposed to be
explained by the existence of God, then we merely push the question
back to why there exists a God rather than no God. If, on the other
hand, God’s existence is self-explanatory or stands in need of no
explanation, then we should in principle be able to say the same for
the existence of the actual world with or without God superadded to
the ontology.
2
The real difficulty in the proposal is that it does not contribute to
understanding what it means for something to exist to know that it
exists because of God’s will. Perhaps there exists a God and the exist-
ence of the actual world is God’s handiwork. Still, what does it mean
to say that the world exists as a result of God’s will? Nor does God’s
choice explain why there exists something rather than nothing if we
do not know why God decided to actualize the world. It does not
solve the problem to learn that God necessarily exists, which in any
case is a conclusion, if it can be attained at all, that belongs to applied
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 121
rather than pure philosophical ontology. There are said to be many
necessarily existent entities in several different branches of applied
scientific ontology, including numbers, sets, propositions, universals,
properties, relations and the like, and we do not suppose that the
existence conditions for such abstract entities, if indeed they exist,
stand in no need of explanation or justification. Why should God’s
existence, if indeed God exists, be an exception in a methodologically
circumspect ontology?
If neither philosophical nor applied scientific ontology is suffi-
ciently enthusiastic about the existence of God, it remains possible for
believers to reaffirm the frailty and hubris of human intellect, and to
interpret the exclusion of God from a preferred existence domain as a
greater opportunity for the expression of personal faith. In philo-
sophical ontology, even if we had a more purely philosophical argu-
ment for the existence of God, it does not seem to add anything to our
understanding to say that God wills the existence of something rather
than nothing. It is not very informative to claim that God is a self-
creating, self-sustaining being who wills to break the logical deadlock
over the existence versus nonexistence of anything in favour of exist-
ence. The existence and will of God cannot explain the existence of
all entities, unless God’s existence is self-explanatory. It is hard to
know how such an assertion is supposed to be interpreted. To the
extent that the concept can be clarified, it offers at best an incomplete
answer to the fundamental question of pure philosophical ontology
that could equally be applied to a self-creating self-sustaining Godless
universe. If we say that it is God’s will to decide the existence or non-
existence of the actual world, then we are left with what is if anything
a more difficult unresolved issue of why God chooses to actualize
rather than not to actualize a world. As far as our limited knowledge
of God’s ways are concerned, it seems that God, who is usually imag-
ined to have unlimited freedom of choice, either will or will not create
a world, let alone our world, let alone as a logically contingent world.
God’s reasons are no doubt inscrutable to mortals, but the idea that
the actual world in all its complexity exists because God wills its
existence lacks a non-circular application in pure philosophical or
applied scientific ontology.
Odds of existing and the Big Bang singularity
If our previous reasoning has been correct, and we can only justifiably
approach the problems of pure philosophical ontology with logic, we
continue to confront the same two possibilities. An actual world,
122 ONTOLOGY
although not necessarily the actual world in its existent state, either
exists or does not exist. Each of the two possibilities, furthermore, as
we have assumed, has a precisely equal 50–50 random probability of
prevailing over the alternative. That a world exists in fact we know
well enough. The mere fact of existence by itself unfortunately does
not answer the question of being or explain why there exists some-
thing rather than nothing.
What consideration could shift the weight of probability from one
side to the other, and help thereby to account for the existence of an
actual world? We should pause at precisely this point, because we are
already beginning to adopt a misleading model of the logically equal
probability of the existence of something versus nothing at all. The
existence of a world or of the actual world as it exists does not have to
win out even in any sort of logical struggle with nonexistence in order
for something rather than nothing to exist. Existence is not earned or
brought into being by an act of will, divine or diabolical, nor is it
explainable philosophically as a cosmic-mathematical “singularity” in
a Big Bang theory of the origin of the universe. Why did God will
existence rather than nonexistence? Why did the Big Bang occur
rather than not occur?
These stubborn questions remain when religion or scientific
cosmology as exercises in applied ontology try to usurp the explana-
tory jurisdiction of pure philosophical ontology. The Big Bang in
particular is powerless to explain why there exists something rather
than nothing. What is meant by the Big Bang is merely an observation-
ally and mathematically supported retrodiction about the origins of
the physical universe. The Big Bang is the initial event that breaks the
50–50 deadlock between the equal random probability of the world’s
existence rather than nonexistence. There is no logical or metaphysi-
cal necessity to the world’s physical existence progressing from a
cosmic singularity at the moment of the Big Bang. According to Big
Bang cosmology, all spacetime and matter explode forth from a single
geometrical point that, paradoxically in relativity physics, is not yet
spatiotemporal. As far as pure logic is concerned, or pure philosophi-
cal ontology considered independently of the question whether its
problems can sensibly be considered by a discipline other than pure
logic, there is no sufficient reason why the 50–50 chance of existence
or nonexistence for an actual world could not equally be broken in
favour of existence without the occurrence of the Big Bang, but, for
example, by the instantaneous distribution of matter throughout the
physical universe without expansion over unfolding spacetime from a
geometrical singularity.
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 123
The Big Bang, as a description of the occurrence and material
evolution of the actual physical world, is itself precisely the contingent
existence that pure philosophical ontology needs to explain. As such,
it can hardly be expected to account for why there exists something
rather than nothing. If the Big Bang were said to occur within an
absolute spacetime receptacle, like that described in Plato’s dialogue
Timaeus as the choron, or like the absolute space and time grid of
Galileo, Descartes, Newton and Leibniz, which Newton in his Opticks
refers to picturesquely as God’s visual field, then perhaps we could
make sense of its occurring at some definite absolute metaphysical place
and time.
3
The Big Bang is supposed to spew forth all of spacetime and
the total energy convertible into material substance that the actual
physical universe will ever contain. The vast material world expands
into the space it creates for itself from a single originally locationless
point. It appears all at once, in one convulsive go, and everything that
happens thereafter is the consequence and development under natural
laws of the first great burst of energy, expanding in complicated inter-
nally interacting ways, and possibly contracting upon itself again with
a rhythm of systole and diastole. The theory by itself does not explain
why the Big Bang took place rather than failed to take place, other than
as a matter of sheer random probability. If the reason why there is some-
thing rather than nothing is the 50–50 probability of physical
spatiotemoral existence occurring, then the Big Bang itself is not the
answer. The Big Bang describes how the universe may have happened
to come into existence, but does not tell us why.
The effort to explain why there is something rather than nothing as
a cosmic crapshoot is tempting in some ways because it holds out the
promise, unfulfilled in the end, of explaining not only why there exists
something rather than nothing, but why the actual world happens
contingently to have the exact state and condition in which it exists. It
might explain, if it explains anything at all, why the actual world is
logically contingent in all its physical states of affairs in roughly the
same way that it tries to answer the question why there exists something
rather than nothing. If it is a random occurrence that an actual world
exists rather than nothing at all exists, then it is surely no stretch to
conclude further that the actual world in all its detail with all its
particularity of entities, facts, states of affairs, events, laws, history, past,
present and future, is logically contingent, equally an outcome of blind
undirected chance. The latter part of the explanation, as it relates to the
main problem of this chapter, is, we maintain, basically correct. It is also
detachable from the fruitless attempt to explain why there is something
rather than nothing as a consequence of random 50–50 probability.
124 ONTOLOGY
If the two problems are separated in this way, an obvious question
is why the logical contingency of the actual world is explainable as a
chance outcome. How, in particular, can the logical contingency of
the actual world be explained in terms of logically random processes
when the existence of an actual world, of something rather than
nothing, is combinatorially logically necessary? The combinatorial
pure philosophical ontology we have developed justifies the distinc-
tion in an intuitive way. We do not say that there is something rather
than nothing because of chance, but as an implication of logical neces-
sity. A combinatorial ontology implies that logically there must be a
logically possible maximally consistent states-of-affairs combination,
which is how the theory defines the concept of an actual world.
There is something rather than nothing because there must be some-
thing rather than nothing. Logically, there must be exactly one
maximally consistent object–property or states-of-affairs combination.
The particular logically possible combination that turns out to be
maximally consistent, on the other hand, is a function of random
probability, with every possibility of maximal consistency sharing equal
weight, and none holding advantage over any other. The probability in
the combinatorial as opposed to the 50–50 logical probability solution
is in one way the same in assigning an equal probability for every
possible outcome. The combinatorial theory is preferable because it
necessitates and does not merely make possible the actual existence of
the actual world, but distributes equal probabilities over all the indefi-
nitely many combinations that might have turned out to be maximally
consistent, over all logically possible worlds, the actual world and
merely logically possible worlds alike. If Leibniz had appreciated the
force of the concept of maximal consistency in answering the question
why there is something rather than nothing or the ultimate origin of
things, he would not have needed to invoke God to explain why there
exists an actual world. Leibniz could then have explained the particu-
larity of the actual world that happens to exist as a pure matter of
chance without slipping into the problematic conclusion that the actual
world in all its unevenly distributed poverty and pain is theologically
the best of all logically possible worlds. Perhaps Leibniz did understand
this implication and deliberately avoided its solution in order to make
God necessary to his metaphysics. We can continue to speak meta-
phorically of God’s choice of the particular maximally consistent
states-of-affairs combination that constitutes the actual world. When
pressed, however, the most reasonable explanation we can offer is that
the condition of the actual world, the entities and states of affairs by
which it is constituted, is entirely a result of chance.
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 125
Chance existence of the actual world
To speak of the actual world is already to single it out from other
worlds or other ways in which the world might have been if a differ-
ent combination of possibilities had been realized. For a variety of
reasons we might prefer a pure philosophical ontology in which
necessarily we are uniquely existent entities, with no actually existent
duplicates of ourselves having adventures in other actually existent
worlds. Intuitively, we cannot easily make sense of the identity con-
ditions that would need to hold for our doppelgängers and ourselves,
even if on the present assumptions we and our counterparts inhabit
distinct logically possible mutually inaccessible worlds.
Can we limit the logically possible worlds, to select just one, the
one that we ontologists happen to occupy, as the actual world? We
might appeal to a more general non-Heideggerean notion of Dasein,
the Modalmoment of “full-strength factuality”, or Plato’s Form of
Being, a property among other properties to enter only into some and
not into all objects’ property combinations, and thereby into the
states-of-affairs combination that constitutes the actual world. Why
not just include Being as a property to be blended combinatorially
into some property combinations with whatever other properties
constitute the Blue Mosque, and as missing from other property
combinations, like those that constitute the Golden City of Eldorado?
It does not enhance our understanding of why something exists rather
than fails to exist to be told that an object possesses or participates in
Dasein, das Modalmoment or Being, for these only give a name to the
factor that needs to be explained. That an object or state of affairs or
world actually exists is taken for granted when we ask why it actually
exists and what it means for it to exist as part of the actual world. A
good explanation is not forthcoming unless we can better say what it
means for an object to possess or participate in Dasein or das
Modalmoment, or a blending of Forms including Plato’s Form of
Being. It similarly adds nothing to a thing for it to be; for its total
predicational constitution, identifying it as the unique individual it is,
either entails its existence or nonexistence. Its property combination,
the unique collection of extraontological predications that constitutes
the object, is either predicationally consistent and complete, that is to
say, maximally consistent, or it is not. If it is maximally consistent,
then the object is an existent entity. If not, not.
An extraontological property, as the name implies, is a property
that by itself does not entail anything about an object’s ontic status,
and that is not instantiated unless the relevant property combin-
ation is maximally consistent. To maintain that existence does not
126 ONTOLOGY
characterize any object says, in short form, that the object’s property
combination is maximally consistent with no predicational gaps only
if, for any extraontological property or property complement, the
combination includes either the extraontological property or its
complement, but not both. If Kant’s criticism of Anselm’s ontological
argument for the existence of God is correct, it implies that Being is
not a property that can be added into a property combination to make
the object qualify as existent, at the risk of never being able intelligibly
to say that the very same numerically identical object either exists or
does not exist. The objects by hypothesis will be constitutionally
different, in that case, because one has while the other does not have
the property of Being in its property combination. We cannot adopt
Plato’s Form of Being as the extra ingredient needed to make the
object associated with a property combination actually exist. The
concept of existence is primitive in that type of theory, precluding any
informative answer to the question of being.
Why is there a material world? How did it come to exist, and why
is there not instead of the existent physical world an empty void with-
out a single material entity? Here is one follow-up answer that we
may find perfectly correct as far as it goes, but not entirely satisfying.
There are just two possibilities to consider: one in which contingently
nothing material exists, and another in which, again contingently,
there exists something rather than nothing. That there should be
physical entities rather than none in these terms has a 50–50 random
probability of occurring, as does the opposite possibility that nothing
whatsoever exists. With these generous odds, especially if we assume
that a logical principle of excluded middle holds, whereby, necessar-
ily, either something or nothing exists, the existence of the material
world can be considered a matter of probability. There is then, by
sheer chance, a material world rather than nothing, and the material
stuff within it has as a matter of fact developed into galaxies and star
systems and all the concrete physical entities whatever they are
existing generally throughout the universe. There might have been
nothing rather than something, at which point it may finally be appro-
priate for scientific ontology to remind philosophical ontology, as
Heidgegger in effect does, that in that event there would be no minds
to ask or try to answer the question.
We might think of the imaginary nonexistence of the physical
world on the model of a spacetime receptacle that is completely
empty of any physical entities. If this way of approaching the problem
is accepted, then we might think of the 50–50 random probability of
the material universe coming into existence within the spacetime
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 127
receptacle as the two equally probable logical possibilities of a mate-
rial world existing or not existing tried out successively over time, like
separate rolls of dice, with nonexistence coming up on every roll until
existence through blind chance finally gets its way. Although scientists
and philosophers sometimes claim to understand the concept of
totally empty, which is to say absolute materially unoccupied, space-
time, it is a consequence of modern relativity physics that the
spacetime continuum is determined by the distribution and relative
motion of physical matter in large gravitational fields. One implica-
tion of a relativistic cosmology is that spacetime itself comes into
existence only with the existence of the physical substance of the
world. If a relativistic scientific ontology seems most correct, it
further implies that the physical existence of the world cannot be
adequately explained as an occurrence at a particular place or within
a particular period of time, and that space and time are themselves
existent entities whose contingent existence needs to be explained in
a complete scientific ontology.
Combinatorial roulette
As the name alone implies, logical objects are identically distributed
or available for combination with logical properties alike in all
logically possible worlds, including the actual world. It is part of the
concept of a logical object or predicable that it not be specific to any
particular logically possible world, but stand as one of the logical
building blocks of any logically possible world.
Is it conceivable, then, even if logical objects are the same in every
logically possible world, that the stock of simple physical entities, if
any should turn out to exist, in addition to the physical states of
affairs involving physical entities, might vary from logically possible
world to logically possible world? In its atomic and quantum theories,
modern science is ontologically committed to the existence of physi-
cally atomic entities defined in terms of energy fields from which
more complex physical structures are composed, in a cosmic assembly
line that takes quarks and atoms to make molecules and macro-
physical entities, star systems, galaxies and, finally, the entire physical
universe. It does not try to say whether precisely the same atomic
units of matter as individual entities or types of entities must exist in
the physical states of affairs of every logically possible world.
Some of these questions cannot be competently answered unless or
until we have progressed to a sound applied scientific ontology. We
can nevertheless relax the conditional framework of these conclusions
128 ONTOLOGY
by remarking that the logical contingency of the actual world is
implied by the fact that it is a combinatorial logical possibility for
complex physical entities to be combined out of simpler entities, from
objects to states of affairs to entire worlds. Whether or not the actual
world consists of physically atomic physical entities, combinatorially,
at least some logically possible worlds involve a logically possible
physical order that is physically constituted by a compositional hierar-
chy of physical simples and complexes, and at least some other logi-
cally possible worlds do not. It does not matter whether the actual
world in point of fact belongs to one category or the other, whether it
is physically composed of physical simples or not; it is certain as a
result to be logically contingent whatever its constitution.
Logically, there must exist an actual world. It need not have been the
actual world as it happens to exist. As far as logic is concerned, the fact
remains that of all the logically possible worlds that might combinator-
ially have involved a maximally consistent property combination, of
properties predicated of or possessed by logical objects; any could
actually have turned out to be maximally consistent. This makes it logi-
cally altogether a matter of sheer blind chance what particular logically
contingent entities and states of affairs happen to exist in the actual
world. Any fact involving any physical spatiotemporal state of the actual
world might have been different than it happens to be. The actual world
we inhabit, sufficiently hospitable to sustain the existence of thinking
creatures such as ourselves, in all its specific details of facts and events,
the distribution of matter and natural laws that govern the physical
entities and their properties throughout the vast universe, is, logically
speaking, purely a function of random probability.
If the nature of the actual world is a result of pure chance, it might
be wondered whether the existence of any actual world is also
random. We have previously argued that the existence of an actual
world, although not the actual world in all its particularity, is logically
necessary by virtue of being a combinatorial possibility. If there were
an argument to show that the existence of something rather than
nothing is merely logically contingent, it would throw all of our
previous reflections into doubt, and cut the ground from under our
logical combinatorial explanation of why there exists something
rather than nothing. Here we consider another purely logical justifi-
cation for the existence of something, an actual world, rather than
nothing. Although the argument, based also on chance or random-
ness, is ultimately found to be incorrect, it affords a worthwhile
opportunity to contrast the logically necessary existence of something
rather than nothing with the logical contingency of the actual physical
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 129
state of the actual world, the existence of an actual world with the
condition of the actual world.
We begin by assuming that logically there is a 50–50 random prob-
ability for something rather than nothing to exist, and of course for
nothing whatsoever to exist rather than something. In many applica-
tions of inductive reasoning, a 50–50 chance of something occurring
is often considered explanatorily adequate to account for its exist-
ence. If the breakdown of a machine is predicted to have a 50–50
chance of occurring, and then in fact subsequently breaks down,
many persons will judge that the machine broke down because, after
all, it had an even chance of doing so, and things could have gone
either way. Indeed, we often regard it as a sufficient explanation of
something’s occurring for there to be a much smaller probability. We
knew that there could be a storm today, the meteorologist said there
was a 30 per cent chance, and, behold, it happened. One might
conclude that the same type of reason might apply in the case of there
existing something rather than nothing. After all, logically and
probabilistically speaking, things could go either way. If God tosses a
coin – heads a world exists and tails no world exists – then we might
end up with a world rather than no world. A world exists on this
account purely as a blind chance occurrence or roll of the cosmic dice.
Equally, from this pure logical standpoint, a world might not have
existed. Then, of course, we would also not be here to think or talk
about it; although the fact of personal existence can no more be
invoked in this context than in other attempts to answer the question
why there exists something rather than nothing. It is a fact that is out
of place in pure philosophical ontology, and a consideration that in a
different guise circles back again to Heidegger’s appeal to the
phenomenological concept of specifically human being-in-the-world
as a way of answering the question of being.
The 50–50 logical possibility or random probability of the exist-
ence of the universe, mapping as it does onto some interpretations of
excluded middle or non-contradiction, is altogether an explanatory
non-starter that does not help us to understand why something rather
than nothing exists. Why, we still want to know, does an actual world
actually happen to exist rather than not exist? Why has existence with
precisely equal random or logical probability in its favour won out
over nonexistence? We should note that in the case of the weather
forecast, there is more behind the probabilistic prediction that a storm
will occur than random probability, even if the forecast predicts a
precisely 50–50 occurrence on the basis of extralogical considera-
tions. There are all the facts about global and local weather patterns,
130 ONTOLOGY
scientific records of past occurrences of storms in similar geographical
circumstances and during the same season, satellite monitoring of
atmospheric conditions, and all the other data that are used to make
predictions about the weather. The same is true to an even greater
degree in the case of the machine’s breakdown, for which we should
in principle be able to provide a rather detailed mechanical explana-
tion. In both the weather and the machine case, we seem to be saying
something substantive about the prior causal condition of a system
such that at a relevant earlier time we could not have judged from the
information available then whether or how the system would change.
We might find that the factors on both sides of opposite predictions
precisely cancel each other out, so that we say the change has a 50–50
chance of occurrence. If that idea makes sense, then we might try to
apply a slightly modified version to the question of whether the
universe as a whole, for purely logical reasons, has a precisely 50–50
chance of existence or nonexistence.
The probability statement in the case of the weather forecast or a
machine breaking down is in a way a kind of summary of all this infor-
mation and reasoning, and is not supposed to stand on its own as an
explanation of why something occurred rather than failed to occur.
This is in sharp disanology with the attempt to explain why there
exists something rather than nothing as a result of random probabil-
ity, for in that application there is naturally no background informa-
tion or history of similar events on which to rely. We are trying rather
pathetically to explain why the universe exists rather than fails to
exist purely on a logical basis of equiprobability for an event to occur
or not to occur, which in this context is at least as if not more reason-
ably interpreted as admitting that we simply have no explanation at
all. To say that a universe sprang into existence, as in the Big Bang,
because probabilistically it could have done so, does not begin to
explain why it actually did. We know before we ask the question that
the world could have existed, because we know before then that the
world in fact exists.
The actual world exists because the physical objects described as
belonging to non-actual merely logically possible worlds are constitu-
tionally incomplete, lacking in some physical property or its comple-
ment. Were it otherwise, then combinatorial pure philosophical
ontology implies that the objects in question would actually exist.
Does the random combination of objects with properties preclude the
possibility of many complete physical objects in actual physical states
of affairs in non-actual merely logically possible worlds? Why do all
the complete physical objects wind up in one world? The reason,
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 131
previously explained, is that all physical objects in a world construed
as a states-of-affairs combination are constitutionally incomplete if
any physical object in that same world is constitutionally incomplete.
Hence, none of those world’s physical states of affairs is actual. It
follows that there is at most one world where all the properties and
relations fall out combinatorially so as to constitute an actual world
consisting of actually existent physical states of affairs involving actu-
ally existent physical entities. There are so many ways in which the
actual world might have been, but only one that logically happens to
be predicationally maximally consistent. The actual world does not
earn the right preconditionally to exist. One world must and only one
world can actually exist; but which one happens to exist is not a
matter of logic or pure philosophical ontology. That is the fundamen-
tal question of applied scientific ontology, for which the answer is,
from a logical point of view, pure chance.
Philosophical implications of the world’s logical contingency
The logical contingency of the actual world, implied by combinatorial
pure philosophical ontology, vouchsafes several important conclusions
for other areas of philosophy that require a correct ontology as foun-
dation. We assume that the actual world as studied by natural science
is logically contingent, and that any of its specific facts, events and
natural laws are logically contingent rather than logically necessary. The
contingency of the universe is also presupposed as a necessary but not
sufficient condition for the freedom of action and the will. The freedom
of will is by no means universally accepted by scientists and philoso-
phers, but in some philosophical theories is believed to provide an
essential assumption for the possibility of moral responsibility.
Needless to say, the logical contingency of the actual world, and even
the logical contingency of the natural laws that govern causal connec-
tions of events in the universe, do not entail the causal contingency of
human thought and action, which is often regarded as the stronger
sense of contingency required for a robust concept of freedom. As we
know, not all philosophers accept the idea of moral responsibility
anyway, and are just as happy to have it eliminated. Others, committed
to the logical necessity of the actual world in all its particularity, face the
difficulty of trying philosophically to reconcile the logical necessity of
the universe with the possibility of the freedom of will and moral
responsibility. This is not a light burden, and philosophers who hope to
make room in their systems for freedom and responsibility ought to
appreciate the advantages of a combinatorial pure philosophical
132 ONTOLOGY
ontology in upholding at least the logical contingency of the actual
world. We do not want to make pure logic the science of the world,
although Leibniz, Hegel and, arguably, the early Wittgenstein tried to
do so, even if logic should turn out to be an ultimate and in other ways
more fundamental discipline than natural science.
Logic is important; but not so important, and not in this way. If we
expect science to be logically contingent because we believe that the
world is constituted by logically contingent states of affairs, then we
should appreciate the explanation of this feature of the actual world
entailed by a combinatorial pure philosophical ontology. What we
know for certain is that some number will come up in combinatorial
roulette for a particular maximally consistent states-of-affairs combi-
nation. Unless the game is fixed, however, we do not know which
number it will be. It is the same in combinatorial pure philosophical
ontology. Sub specie aeternitatis, from an imaginary god’s-eye point
of view outside and surveying the whole of the existent universe, we
know that there must be something rather than nothing, that there is
certain to be a maximally consistent states-of-affairs combination or
object–property combination; but, importantly, we do not know
which. The actual world that happens to exist is a function of pure
chance on the proposed combinatorial theory the world we happen to
tenant, whose secrets we try to discover in natural science, is the logi-
cally contingent result, so to speak, of a single turn of the combinato-
rial wheel.
The logical analysis of being says, in effect, that in this special case,
because of the combinatorial possibilities of pure classical logic, if an
actual world is logically possible, then an actual world is logically
necessary. The modal status of the actual world is logically contingent,
from a logical point of view a matter of pure chance. It may neverthe-
less turn out to be physically determinate, and in that sense physically
or causally necessary, and hence a matter once again of physically or
causally circumscribed probability. This is partly an issue for scientists
to decide. Newton and Leibniz opt for the necessity of the actual
world – Leibniz in the very strong sense of his logical-metaphysical
concept of necessity and identity, Newton in terms of absolute space
and time and deterministic applied mathematical laws of motion,
acting on a random distribution of material substances. Later scien-
tists, from Einstein to Stephen Hawking, with Werner Heisenberg,
Paul Dirac, Pierre Duhem and others in between, have regarded the
universe as logically contingent and physically-causally indeterminate
not only in its physical states of affairs, but in the natural laws by
which physical phenomena are governed.
WHY ONE L OGI CAL L Y CONTI NGENT ACTUAL WORL D 133
It is no more remarkable – and no less – to think that, of all the
different logically possible worlds that might have been actualized as
maximally consistent states-of-affairs combinations, we happen to
exist and are able to consider these abstruse topics of metaphysics, to
suffer and enjoy the moments of our lives, than it is to think that of all
the possible galaxies and star systems in the actual world we just
happen to have been born on planet Earth. It is not that remote from
the amazement we can produce by reflecting that of all the many
kinds of terrestrial animals, we just happened to evolve as members of
the species homo sapiens sapiens, or that we happen to be born of one
family in one part of the actual world at a certain time in history in our
physical world’s spacetime. There is no necessity to any of these
occurrences, logical, causal or any other type, except the conditional
necessity that were it not for the logically contingent pure random
chance satisfaction of all of these conditions – being in a hospitable
logically possible actual world, on a hospitable planet in all that vast
world, being genetically members of the human species and of a
certain race and gender and age and biological family – we would not
now be entertaining these thoughts. We would not be able to, for we
would not be.
Now, look about; it’s okay. You exist, and so does everything
around you in the actual world. And existence is very important – just
try to get along without it! Something rather than nothing must have
existed, but it need not have included you or me. We exist entirely as
a gift of chance – it is in every way a fragile thing.
Concepts of existence in
philosophical logic and the
5 analysis of being qua being
Logic, predication, existence
What can logic teach us about ontology? Symbolic logic in and of
itself is not that philosophically interesting, but reveals something
important when, appropriately interpreted, it serves to explain why
there is something rather than nothing. Logic embodies a set of
concepts and philosophical commitments about what it means for
something to exist that can be recovered from the expressive capabili-
ties of logic in the predication of properties to objects.
We have argued that logic supports a non-circular a priori answer
to the question of being, of why there is something rather than noth-
ing, and why there exists exactly one logically contingent actual
world. The rules of formal symbolic logic, concerned primarily with
the normative requirements of deductively valid inference, do not
entail that any given specimen of actual reasoning conform to its
truth-conditions, let alone that any contingently existent entity in the
actual world actually exists. Logic seems ontologically impotent in
this regard only if we focus exclusively on the inference mechanisms
of formal logical systems. For purposes of pure philosophical ontol-
ogy, there is much more to be learned from the expressive capabilities
of classical logic, whether Aristotelian syllogistic, Boolean algebra or
modern symbolic first-order predicate logic.
Logic is easily interwoven with pure philosophical ontology
because pure philosophical ontology, like logic, is purely formal, and
because it is only as a discipline and not as an ontic domain that logic
is called upon to answer the Heideggerean question of being. An
obvious objection to the combinatorial analysis of the concept of
existence is that if Heidegger’s phenomenology is too rich for ontol-
ogy, if it is already so anchored to the existence of contingently
existent actual entities like ourselves, our time horizons, and our
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 135
experience of being in the world, is formal symbolic logic not too
impoverished? If the existentialist ontology that results from accept-
ing phenomenology as the method by which to answer the question of
being cannot provide a non-circular answer to the question of what it
means for something to exist without presupposing the existence of
contingently existent things like human beings and times, or their
experience of the actual world, then we must worry about the pros-
pects of making logic too thin a basis for an a priori explanation of
what it means for something to exist. As a system of pure expressive
and inferential forms, logic is devoid of substantive ontic content. It
does not offer enough to “deduce” real existence, whatever that could
mean. We cannot logically derive the existence of apples or camels, or
of any other entities in a preferred existence domain, which is the
business of applied ontology. The fact that logical form includes all
logically possible combinations of all logically possible objects with all
logically possible properties is nevertheless enough to explain the
concept of being and answer related questions of pure philosophical
ontology.
Ontology by numbers
It will not avail, for this reason, simply to take note of alternative
applied scientific ontologies, and try to say that what it means for
something to exist depends on which ontology we accept, as though it
were a matter of joining a political party. Plato says one thing; David
Hume another. Other philosophers, before and after and in between
Plato and Hume, have proposed ontologies different from one
another yet again. We may decide to enter the dispute, dissatisfied
with the available choices, and thrash out our own applied scientific
ontology as a further alternative. Even then, if we have not first
clarified the concept of being, we can only say, as we point to the
items on a list of entities, that this is what it means for something to
exist – to be included on the list. It should be obvious by now that this
way of proceeding is improper methodology, especially if we agree
that pure philosophical ontology has logical and explanatory priority
over the questions of applied scientific ontology.
We get nowhere with respect to the problems of pure philosophical
ontology, in understanding what it means for something to exist, by
choosing, say, a Platonic over a Humean ontology, or the reverse, or
by advancing our own preferred applied scientific ontology. To main-
tain with Plato that only abstract entities are real is to declare our
agreement with a particular applied scientific ontology, with a
136 ONTOLOGY
preferred existence domain. The same is true if we accept an entirely
different austerely empiricist ontology like Hume’s, in which to be
real is to be experienced in immediate thought, beyond which we
have no knowledge of reality. Here too we have only signed on to
what we believe is a more attractive applied scientific ontology. We
can never address the problems of pure philosophical ontology from
an applied scientific standpoint, because we cannot understand what
it means for something to exist merely by considering an inventory of
existent entities. We can never satisfactorily answer the questions of
pure philosophical ontology by invoking solutions that are endemic
to the specific preferred existence domains of applied scientific ontol-
ogy. Nor can we intelligently compile a description of existent entities
in the first place if we do not know what it means for something to
exist, if we have no principles to guide our choices as we consider
what things exist or do not exist.
The sign of these priority inversions is that we stumble immedi-
ately over the fact that alternative applied scientific ontologies reflect
entirely different, even logically incompatible, concepts of what it
means to exist. Why are we Platonists rather than Humeans, or
Humeans rather than Platonists? Why do we gravitate toward a realist
ontology, or the reverse? We are forced to adjudicate between
extreme ontological alternatives because both Plato and Hume
cannot both be right while supporting such different conclusions
about what kinds of things exist. If we can explain what it means for
something to exist by holding up a good-looking list of supposedly
existent entities, then it is equally legitimate for an opponent to hold
up a different list, and maintain on the contrary that to exist is to be
included among its itemization of very different existent entities. This
is precisely what happens when philosophers challenge one another’s
applied ontologies of preferred existence domains without first
having answered the question of being. We cannot intelligently say
that this exists and that does not exist if we have not first satisfactorily
explained what it means for something, anything, to exist.
The point is that we must first answer the most basic questions of
pure philosophical ontology, and then, armed with an understanding
of what it means in the most general terms for something to exist,
proceed to apply the concept of being to work out the details of an
applied scientific ontology. If we get to that crossroads, then we have
a chance of deciding objectively whether Plato or Hume’s applied
ontology is more correct, committed to an extant domain of existent
entities, and reflecting a considered pure philosophical concept of
existence. Otherwise, the most that we can do is salute one applied
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 137
scientific existence domain or the other on instinctive grounds, with
no understanding of what it means for something to exist.
1
We might find it gratifying to rescue Plato or Hume from the
suspicion of having confused pure philosophical with applied
scientific ontology. We could try to do so by pleading that they cannot
reasonably be charged with inverting these components of ontology if
they never recognized the problems of pure philosophical ontology as
meaningful or tractable in the first place. Perhaps they made progress
instead in the only way they thought possible by spelling out the
details of their respective preferred existence domains. If so, neither
Plato nor Hume offers an edifying model of how an integrated
philosophical–scientific ontology ought to proceed, and we should
once again avoid consulting either of their conflicting applied scien-
tific ontologies in order to address what, by hypothesis, we properly
regard as a fundamental question of pure philosophical ontology. We
must say the same for any other ontologists who try to avoid explain-
ing the concept of being.
Modality of combinatorial ontology
We have proceeded differently, by defining the concept of being in
purely logical terms, and arguing on the basis of a combinatorial
analysis of existence that there must exist exactly one logically
contingent actual world. The inferences we have proposed have
been informally presented, relying on an intuitive understanding
of the implications of the idea that to exist is to be maximally con-
sistent.
The modal structure of the arguments we have offered to answer
the question of being, to explain why there exists something rather
than nothing, and why there exists exactly one actual world that is
logically contingent in all its physical states, should now be formal-
ized. Doing so provides an opportunity to review all three of the
explanations that have been offered in combinatorial pure philo-
sophical ontology, to see precisely how they are related, and to recon-
sider their conclusions.
2
A critic might imagine that the inference used to explain why there
exists something rather than nothing contains a modal fallacy. The
claim that the combinatorial possibilities for a logical object to
combine with a logical property in pure classical logic logically neces-
sitate the existence of an actual world that can then be shown to be the
uniquely existent logically contingent actual world may seem modally
problematic. The uniquely existent actual world is supposed to be
138 ONTOLOGY
logically contingent, despite the fact that its existence is proved by the
combinatorially logically necessary existence of an actual world. Is
there not something wrong here?
The fallacy seems to be that, for any proposition p, if it is logically
necessary that it is logically possible that p, then it is logically neces-
sary that p. Let w
@
be substituted for p by virtue of representing a
conjunction consisting of all the propositions that are true in and of
the actual world. Then it looks as though by claiming that from the
fact that it is logically necessary that there be a maximally consistent
combination of states of affairs in the totality of all logically possible
states-of-affairs combinations we can logically infer that combinator-
ially an actual world necessarily exists. It is a modal fallacy to permit
the deductively invalid inference, ~•p | ~p, or the false conditional,
~•p ÷ ~p, even in the strongest sound systems of iterated modal
logic. A counter-example to remind us of how the statement goes
astray can be given in modal system S
5
. There we are permitted to
infer ~•p from •p. Let p be the logically possible proposition that
pigs fly. Then it follows in S
5
that ~•p, but not, even in S
5
, that ~p,
that it is logically necessary that pigs fly. This, fortunately, is not the
modal structure of the argument we have advanced, which is modally
and in other ways logically more complicated.
3
To explain how the fallacy is avoided, we formalize the underlying
modality of the arguments by which we propose to demonstrate
combinatorially that logically there must exist something rather than
nothing, that an actual world logically must exist, but that the condi-
tion of the actual world is not logically necessary. We refer to the
actual world as an individual entity, w
@
, and apply a special modal
operator to represent the actuality of any logically possible world. For
this purpose, actuality is symbolized by A, within a standard alethic
modal logic. We assume, as we have throughout, that for a logically
possible world to be actual means for it to be a maximally consistent
states-of-affairs combination, which we symbolize as the metalogical
predicate MaxCon. We allow modal operators to attach directly to
individual propositions or to any conjunction of propositions, and
even to a conjunction of propositions that completely describe a
logically possible world. The distinction makes it possible to formal-
ize the proposition that the actual world is actual, which we write as:
Aw
@
. We can then more formally consider the logic of the previous
inferences used to explain why there exists something rather than
nothing, and why there exists exactly one logically contingent actual
world. Through much of the logical symbolizations to follow we
make intuitive use of the A operator, and only near the end propose
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 139
inference rules supported by the same intuitions for its introduction
in standard first-order predicate logic.
We begin by appealing only to the conditional, œw
i
[MaxCon.w
i
÷
Aw
i
] (or œw
i
[MaxCon.w
i
÷ ›w
k
[Aw
k
r w
i
= w
k
]]). The converse con-
ditional appears in other arguments involving the biconditional,
whereby we more generally formulate the combinatorial answer to
the question of being, œx[MaxCon.x ÷ Ax]. We refer to the con-
ditional or complete biconditional analysis of being respectively as
Df.A ÷ and A ÷. Here, in answering the question why there exists
something rather than nothing, it is important to see that we can
deduce actuality from maximal consistency alone. We note that in
deducing the instantiated consequent, Ao, from the instantiated ante-
cedent, MaxCon.o, we deduce the actuality of o. The universal
implies that we can deduce the actuality of any o, including any real
existent entity, or state of affairs, or combination of states of affairs or
the entire actual world, provided only that, according to the princi-
ple, o is maximally consistent. We can in principle soundly substitute
for “o” anything we can name that is maximally consistent, including
the actual world, w
@
. We prove the actuality of the actual world as a
substitution instance, Aw
@
, if we know that the actual world is
maximally consistent, MaxCon.w
@
. We cannot avoid circularity if we
invoke the converse conditional, Aw
@
÷ MaxCon.w
@
, at this stage of
the argument, in order to conclude that the actual world is maximally
consistent, unless we are in a position to assert what is now supposed
to be proved – that the actual world is actual. What, then, can we do?
It is tempting to try to establish the maximal consistency of the
actual world by means of an argument that we should consider only to
reject. We should not assume that only a maximally consistent world
can be perceived, and then cite the empirical fact that we do in fact
experience a world, whether in sensation or in the experience of the
flow of time in reflecting self-consciously on the fact of thinking, in
order to conclude that the actual world that we perceive must be
maximally consistent. Experiential data cannot count as evidence in
non-circular reasoning to show that the actual world is maximally
consistent. Thankfully, inspection of the states of affairs we experi-
ence is not the only methodology to which we are limited. We are no
more required to survey each state of affairs and consider them in all
their complex relations in order to know that the actual world is
maximally consistent than we are required to go door-to-door with a
questionnaire in order to find out if all bachelors are unmarried. A
single glimpse of the outside world by any of the senses is sufficient to
uphold this argument, if we also hold that only a maximally consistent
140 ONTOLOGY
states-of-affairs combination could possibly or even logically possibly
be perceived. It will not do to dig in our heels and declare that existent
thought cannot be related to what is nonexistent. That assumption, in
the first place, might not even be true; it disguises, in any case, rather
than exposes, the interesting conceptual connections that need to be
articulated in order to explain why only a maximally consistent world
is experienceable. If there is just an eye (and brain), and nothing else
outside it, not even a single light-ray, the eye might still be able to
perceive by virtue of internal changes of state.
We only make things worse if we proceed to argue that there must
be an actual world in order for anything to be perceived, on the
assumption that the fact of perception implies a change of state, and
that there can be no changes of state except in physical space and
time, the lonely eye and brain changing internal states in the impen-
etrable darkness. The trouble is that with each step we are wandering
farther and farther away from pure philosophical ontology into
applied scientific ontology. If we simply stipulate that any experience-
able world is actual, and then argue as above that the experienced
world is the only uniquely existent actual world, then we seem
merely to be insisting on the fact of a connection between experience
and actuality without analysing its meaning or explaining its concep-
tual structure. An argument to the effect that we do in fact experience
the world and that we could only experience a maximally consistent
world is not absurd, but it is also not the best we can do.
Ultimately, we want to be able to maintain that any logically possible
world is actual if and only if it is identical with the actual world, and that
the actual world is nevertheless logically contingent. We quantify alike
over the actual world and non-actual merely logically possible worlds,
even though, as a consequence of our reform of modal semantics, only
the actual world exists. In doing so, we in effect quantify over one
maximally consistent and indefinitely many submaximally consistent
states-of-affairs combinations, which is equivalently to quantifying over
one actualized and many unactualized logical possibilities.
As might be expected, combinatorial pure philosophical ontology
has a non-empirical non-experiential way of proving that the actual
world is maximally consistent. We know that there must exist an actual
world, and we know that there can exist at most one actual world. We
do not try to prove that the actual world, in particular the world we
experience, is maximally consistent, regardless of whatever conceptual
linkages might be adduced. Accordingly, we shall not try to justify the
choice of “w
@
” as a substitution instance for “o” in the definition of
actuality, except by arguing that w
@
is the one and only actual world,
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 141
and hence the only logically possible truth-preserving substitution for
“o”, together with designations for any particular actual states of affairs
or existent entities in w
@
. We require a principle to mediate the appli-
cation of alethic modalities of necessity, possibility and actuality, from
propositions to worlds, particularly because we do not interpret worlds
as proposition sets. Accordingly, we offer the following equivalence to
justify the modality of a logically possible world in terms of the
modality of the propositions true in or of that world, œw
i
[~w
i
÷
œp[p
w
i
÷ ~p]]. Similarly for the modal qualification of a logically
possible world as logically possible or actual, substituting “•” or “A”
respectively for “~”. It is sufficient for present purposes that it is
logically necessary for there to be included in the totality of all states-
of-affairs combinations at least one combination that is maximally con-
sistent. This shows, assuming that only the actual world is maximally
consistent, that the actual world actually exists, MaxCon.w
@
÷ Aw
@
.
We argue that ~MaxCon.w
@
, from which, together with the
assumption that ~œx[MaxCon.x ÷ Ax], we deduce the necessary
actuality of the actual world, ~Aw
@
and ~A›w
i
Aw
i
. We can then prove
œw
i
[MaxCon.w
i
÷ w
i
= w
@
] and œw
i
[w
i
÷ w
@
÷
-
MaxCon.w
i
].
4
Logical solution to the question of being in combinatorial pure
philosophical ontology
We argue that logically necessarily if a maximally consistent states-of-
affairs combination possibly exists, then it exists. The combination
exists as a logical possibility in the first instance, as a logically possible
combination of logically possible objects and logically possible
properties. It is then shown to be actual by virtue of satisfying the
definition of actuality as maximal consistency.
We are logically guaranteed the logical possibility of every logically
consistent states-of-affairs combination. We prove that there must be
a maximally consistent logically possible world, and hence an actual
world. Then we prove that there can be only one uniquely actual
world, from the intermediate conclusion that logically there can be
only one maximally consistent states-of-affairs combination. The
maximally consistent states-of-affairs combination by virtue of being
maximal eats up all the maximal consistency available, depriving
other non-actual merely logically possible worlds of the (especially
relational) object–property combinations they would need in order to
be independently predicationally complete.
For convenience in what follows, we adopt a standard notation
involving restricted quantification over worlds. We consider the
142 ONTOLOGY
modal status of individual propositions and logically possible worlds
alike, on the grounds that a logically possible world can be construed
as a long conjunction of propositions that collectively express all the
states of affairs included in a world’s states-of-affairs combination.
We permit modal qualifications of some of these restrictedly quanti-
fied sentences, where, in an obvious sense, to speak of logical possibil-
ity is already to speak of truth in at least one logically possible world,
and to speak of logical necessity is already to speak of truth in every
logically possible world. Such retranslations are naturally possible,
but not as illuminating as allowing the iterations of both forms of
reference over all or some worlds, to remind us that some of our
assumptions and conclusions are supposed to be logically necessary,
and that these are interpreted by reference to worlds as maximally
consistent states-of-affairs combinations.
We can now further formalize some of these inferences. We add
abbreviations for a function of logically possible combinations
(Combo) of logically possible predication objects (Object) and
logically possible properties (Property), indicating membership in a
combination by the inclusion sign (=). We begin by formalizing the
argument that logically combinatorially there must exist an actual
world – something rather than nothing must exist.
Logically necessarily, there exists a maximally consistent world:
1. ~›w
i
[[MaxCon.w
i
r w
i
= œx|Combo(œy|Object.y,
œz|Property.z).x] ÷ •›w
i
[MaxCon.w
i
r w
i
=
œx|Combo(œy|Object.y, œz|Property.z).x]]
Df. MaxCon
2. ~•›w
i
[MaxCon.w
i
r w
i
= œx|Combo(œy|Object.y,
œz|Property.z).x]] Combinatorics
3. ~›w
i
[MaxCon.w
i
r w
i
= œx|Combo(œy|Object.y,
œz|Property.z).x]] (1, 2)
4. ~›w
i
MaxCon.w
i
(3)
The core of the combinatorial analysis of the concept of being is
that it authorizes deducing the necessary existence of a world on the
grounds that necessarily it is logically possible for there to be a
maximally consistent states-of-affairs or object–property combina-
tion. This, the theory maintains, is what it means for a world to exist.
We expand the inference from 1–4 above by citing the logical
necessity that the mere logical possibility of a maximally consistent
states-of-affairs combination implies its existence, together with the
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 143
proposition that it is logically necessary that it is logically possible that
there exist a maximally consistent states-of-affairs combination.
5
The
argument states:
5. ~[•›w
i
MaxCon.w
i
÷ ›w
i
MaxCon.w
i
] Df MaxCon
6. ~•›w
i
MaxCon.w
i
Combinatorics
7. ~›w
i
MaxCon.w
i
(5, 6 Modal logic)
We note that assumption 5 is not universal, but applies specifically to
worlds or maximally or submaximally consistent states-of-affairs
combinations. Now we apply either conclusion 4 or 7 above to prove:
Why there is something rather than nothing – logically, there must
exist an actual world:
8. ~œx[MaxCon.x ÷ Ax] Df. A÷
9. ~›w
i
Aw
i
(4 or 7, 8 Modal logic)
10. ›w
i
Aw
i
(9 ~p ÷ p, a fortiori)
11. A›w
i
Aw
i
(10 p ÷ Ap, a fortiori)
12. ~A›w
i
Aw
i
(8, 9, 11 Modal logic)
In conclusion 11 we argue somewhat redundantly that an actual
world actually exists. In principle, there need be no limit to how many
times we iterate the actuality operator. Similarly, there need be no
limit to how many times we iterate a possibility operator; in practice,
it is not especially helpful to continue beyond statement 11, by deriv-
ing, as we could, AA›w
i
Aw
i
, AAA›w
i
Aw
i
and so on. Instead, we prove
12, relying only on the necessary truth of propositions 8 and 9, to
derive conclusion 11, which, if the inference is deductively valid,
must be as logically necessary as the two assumptions from which it is
inferred. Thus, we prove that it is logically necessary that there exists
an actual world. Now we formalize the previous argument to establish
the unique actuality of the actual world.
6
Unique existence of the actual world
The proof depends on the assumption that a maximally consistent
combination of all logically possible objects and all logically possible
properties into all logically possible states of affairs is unique. If there
were other states of affairs that could be consistently added to such a
combination, it would not after all be maximally consistent, but at
144 ONTOLOGY
best submaximal. We do not propose to prove formally the unique-
ness of maximal consistency, but to formalize it as an assumption from
which to derive the conclusion that necessarily an actual world is
uniquely actual. This is just to say that logically necessarily there is
only one actual world.
Above, we demonstrated the necessary existence of an actual world
using only the conditional definition, Df. A ÷, ~œx[MaxCon.x ÷ Ax],
and avoided the circularity with which we were concerned. We can
therefore avail ourselves now of the full biconditional combinatorial
analysis of the concept of being, Df. A÷, ~œx[MaxCon.x ÷ Ax], as
provided by Principle 3, to prove the uniqueness of the actual world. As
a lemma, we thereby establish the principal conclusion of modal
actualism in opposition to the modal realism of conventional model set
theoretical modal semantics with its definition of all worlds, including
the actual world and nonactual merely logically possible world, as
maximally consistent proposition sets. The proof is this:
Why there is only one actual world – there can be at most one
maximally consistent world:
13. ~œx[MaxCon.x ÷ Ax] (Df. A÷)
14. ~œw
i
[MaxCon.w
i
÷
-
› w
k
[MaxCon.w
k
r w
i
÷ w
k
]]
(MaxCon Unique)
15. ~œw
i
[Aw
i
÷ œw
k
[Aw
k
÷ w
i
= w
k
]] (13, 14)
Logical contingency of the actual world
It remains to relate the necessary actual existence of an actual world,
~A›w
i
Aw
i
, to the modality of the actual world, w
@
. Can we validly
substitute “w
@
” for “w
i
” in conclusion 12 to obtain ~AAw
@
or ~Aw
@
?
To prove, on the contrary, that the actuality of the actual world is
logically contingent, Aw
@
r
-
~Aw
@
, we appeal to the multiplicity of
logically possible worlds distinct from w
@
. We can be sure of their
multiplicity because combinatorially we cannot collapse all logically
possible worlds into one; there are logically possible combinations of
objects and properties in nonexistent merely logically possible states
of affairs that do not exist in the actual world. If the combinatorial
analysis of being is correct, and it is combinatorially logically neces-
sary that a logically contingent actual world uniquely exists, then
intuitively we expect to be able to prove the logically necessary
propositions:
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 145
~A›w
i
Aw
i
~›w
i
Aw
i
~Aw
@
As, indeed, we can; but not:
›w
i
A~w
i
›w
i
~w
i
A›w
i
~w
i
A›w
i
A~w
i
A~w
@
~w
@
As another way of arriving at the same conclusion, consider the
following argument. We say that a world is maximally consistent
when we write ›w
i
MaxCon.w
i
. This is a shorthand way of saying:
›x[MaxCon.x r x = Comboœy|Object.y, œz|Property.z]
Or, equivalently, where SA denotes a state of affairs:
›x[MaxCon.x r x = Comboœy|SA.y]
It is a conclusion of combinatorial pure philosophical ontology that:
MaxCon.Comboœy|SA.y ÷ Aw
@
We are accordingly entitled to make the following inference, deriving
the de dicto logically necessary existence of something (rather than
nothing, an actual world); the de dicto logically necessary existence of
the actual world; and the de dicto logically necessary actuality of the
actual world:
7
1. ~œx[[MaxCon.x r x = Comboœy|SA.y] ÷ [x = w
@
r Ax]]
Actuality
2. ~›x[MaxCon.x r x = Comboœy|SA.y] Combinatorics
3. ~›xAx [1, 2]
4. ~›x[x = w
@
r Ax] [1, 2]
5. ~Aw
@
[4]
Again, what cannot be proved from any of the assumptions we
have considered is the de re logical necessity of the actual world. It is
true in combinatorial pure philosophical ontology, in other words,
146 ONTOLOGY
that
-
›x~[x = w
@
r Ax] or
-
A~w
@
or
-
~w
@
. We shall now see how
the required restrictions permit the above inferences of the de dicto
necessary existence of the actual world, and prohibit inferences of the
de re necessary existence of the actual world, which would collapse
logical contingency and freedom of action and will into logical
determinacy.
The excluded inferences in the second list contradict the logical
contingency of the actual world considered as one among innumerably
many logically possible worlds that might have existed instead. We
introduce inference rules for the modal actuality opertor, A, formally
defining the modality. Proof of the antitheorem
-
[~Ap ÷ A~p] that
safeguards the logical contingency of the logically necessarily actual
world is then routine but still instructive. Up until this point, we have
relied on an intuitive understanding of the laws of logical inference
governing the delta modal operator A, and have not needed to support
any implications involving its logical properties. We now present
formal inference rules in support of the subsequent demonstration:
Inference rules for modal actuality operator A AA AA
p p p p xp x p
p p p p x p xp
- -
A A A A¯ ¯ A
- -
A A A ¯ A A¯
Proof of antitheorem:
-
[~Ap ÷ A~p]
1.
-
~p Assumption
2. ~Ap Hypothesis for reductio
3. ~Ap ÷ A~p Hypothesis for reductio
4. A
-
~p [1 A Rule]
5.
-
A~p [4 A Rule]
6.
-
~Ap [3, 5 Modus tollendo tollens]
7.
-
[~Ap ÷ A~p] [2, 3, 6 Reductio ad absurdum]
8. Ap ÷ p [A Rule]
9. ~[Ap ÷ p] [8 Necessitation]
10. ~Ap ÷ ~p [9 Modal logic]
11. ~p ÷ A~p [A Rule]
12. ~Ap ÷ A~p [10, 11]
13.
-
~Ap [2, 7, 12 Reductio ad absurdum]
14.
-
~p ÷
-
~Ap [1, 13]
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 147
Let p be a contingently true proposition, that pigs wallow. Then we
have
-
~p in the second assumption, without any argument. It would
be circular, even in this elementary proof context, simply to assume that
-
~w
@
, even though our immediate purpose is not to prove that
-
~w
@
,
but only negatively that ~w
@
cannot validly be deduced from ~Aw
@
.
It is therefore enough to suppose that there is at least one logically non-
necessary proposition that is necessarily actual, in order to show that
there is no valid deduction from necessary actuality to actual necessity.
This is enough to establish the logical contingency of the condition of
the actual world, despite the logical necessity of its existence.
What about ~Ap? Is it obvious that it is logically necessary that
actually pigs wallow? Not in the absence of a combinatorial modal
ontological theory perhaps. We recall that we are dealing not only with
any random proposition p in the case we are interested in, but with the
proposition Ap that in context has been validly derived from two logi-
cally necessary assumptions. As long as the proposition that, or state of
affairs in which, pigs wallow is true of, or exists, in the actual world,
then we are justified in the problem at issue to infer ~Ap from Ap, which
we stipulate accordingly above as the first hypothesis. We prove, even
on the strength of the first hypothesis, proclaiming the logical necessity
of the actuality of p, that we cannot validly derive the logical necessity
of p itself, in the form A~p or ~p, for any proposition p. Thus, an
inference that would threaten the logical contingency of the condition
as opposed to the existence of the actual world, in the sense of the
particular states of affairs that constitute the actual world, is blocked.
What can we say more positively about the modal status of the
actual world’s constituent states of affairs? Is the logically necessarily
existent uniquely actual world also logically necessary in all of its
constituent states of affairs, or is it logically contingent? There are at
least some different states of affairs that distinguish the states-of-
affairs combinations to which they belong as world-variable states.
These are effectively spatiotemporal physical states, which must vary
from logically possible world to logically possible world, discounting
nonexistent or universally distributed abstract states of affairs as
before. The only way for distinct logically possible worlds to collapse
into a single logically possible world would be if the one and only
logically possible world consisted of nothing but abstract logically
necessary states of affairs, such as the truths of logic and mathematics.
It follows in combinatorial ontology that there must be distinct logi-
cally possible worlds. Only one among all logically possible worlds, the
uniquely actual world, actually exists. All others are only potentially
existent, in the sense that they could and would have existed if they had
148 ONTOLOGY
been maximally instead of submaximally consistent. The possibility of
logically possible worlds different in the condition of their physical
states from the actual world is sufficient to uphold the actual world’s
logical contingency. This is an important implication, because if there
were no worlds distinct from the actual world, then the actual world
would be logically necessary in all its constituent states of affairs, includ-
ing all its physical states of affairs. This would clearly not be a conclu-
sion in which to rejoice. The implication is unsavoury not only because
it does not agree with our intuitive interpretation of the contingency of
events in the actual world, but more importantly because it involves an
intrusion of pure ontology this time on applied ontology’s turf. Pure
philosophical ontology, aimed at answering the question of being,
should not dictate terms to applied scientific ontology concerning the
existence of any particular states of affairs. If pure philosophical ontol-
ogy determines that the physical state of the actual world is logically
necessary, then it crosses the line. It implies that the particular states of
affairs that exist in the actual world are the only ones that could logi-
cally possibly be recognized as existent by any competent applied
scientific ontology. In effect, it tries to usurp applied ontology’s work
in advance of completing its own project of explaining what it means
for something to exist.
The physical and mental events with which we are familiar, however
we may later sort out their applied ontology, may or may not be caus-
ally necessary. It would be straining to interpret such occurrences as
anything but logically contingent. I may have baby-blue eyes, but it is
logically possible that, like 60 per cent of all human beings, I have
brown eyes instead. In another world, we can easily stipulate a states-
of-affairs combination in which I have differently pigmented irises. A
little logically possible chromosomal cut-and-paste at the right stage of
my embryonic development is all it should take. The logically possible
brown-eyed me does not actually exist, because that logically possible
me is not maximally consistent in all his (or her?) predications. What
is my height? What is my gender? What is my native language? Am I
friends with Napoleon in that world? Do I learn to fly a helicopter?
What are the further genetic and historical ramifications of altering my
eye colour in another logically possible world? It is one thing to wave
a hand and say, as conventional modal logicians do, that there exists a
logically possible world in which I have brown rather than blue eyes. Do
we ever thereby manage to refer to a predicationally complete world?
Or do we not rather inevitably leave almost all properties of the objects
in such a world unspecified? Why in modal logic should we ever feel the
need to pretend otherwise?
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 149
If the actual world should turn out to be the only logically possible
world, if all logical possibility were to collapse into actuality, we
would still have a logical answer to the question of being. We could
continue even in that extreme case to say that there is something
rather than nothing because there must exist an actual world, where
the actual world in all its physical states is logically necessary rather
than logically contingent. This, we must re-emphasize, is the very
opposite conclusion indicated by a combinatorial pure philosophical
ontology. In a combinatorial framework, the logical possibility of
transworld-variant world-distinguishing physical properties must be
taken into account as among the totality of logically possible combi-
nations of all logically possible objects with all logically possible prop-
erties in all logically possible states of affairs.
The physical states of affairs that we might know about from our
experience of the actual world are real, they happen to exist, but are
not logically necessary. If we trace effect to cause back far enough we
find more and more contributing events explainable only as an out-
come of pure chance. Consider only that your mother happened to
meet your father. Almost every couple has a story of sheer coincidence
to tell about how they came together or how they produced their
offspring. Additional chance occurrences determine whether or not a
woman with child survives the kinds of disease or accidents that
threaten their destruction. The same is true of all spatiotemporal
occurrences involving physical entities and states of affairs in the
actual world. We can, in other words, to answer a previous question,
and we should, authorize the substitution of “w
@
” for “w
i
” in conclu-
sion 12, on the grounds that “w
@
” is our name for the actual world,
whose reference we are entitled to stipulate once we have proved that
there is only one actual world. That the actual world is logically
necessarily actual does not entail that the actual world is logically
necessary. We can now formalize these inferences concerning the
actuality and logical contingency of the actual world.
Why the actual world is logically contingent – there are other
actually nonexistent logically possible worlds:
16. ›w
i
[Aw
i
r w
i
= w
@
] (10 @-Nominalization)
17. œw
i
[•w
i
÷ •Aw
i
] Possible actuality
18. ›w
i
[•w
i
r w
i
÷ w
@
] Multiplicity of •
worlds distinct from @
19. ›w
i
[•w
i
r w
i
÷ w
@
] (17, 18)
20. Aw
@
r ~Aw
@
r
-
~w
@
(12, 15, 16, 19)
150 ONTOLOGY
It is worth knowing that, even in the strongest standard systems of
modal logic, we can validly derive ~›w
i
[Aw
i
r w
i
= w
@
] and ~Aw
@
,
but not ~w
@
. The latter would blatantly contradict the conclusion in
20. Logically necessarily, there exists an actual world; logically neces-
sarily there exists at most one actual world, which is to say the actual
world, w
@
. The actual world is nevertheless not logically necessary
but logically contingent in all its constituent states of affairs, and in
particular in all its transworld-variant physical states of affairs.
8
Unique actuality of the actual world
We now express the unique actuality of the actual world more directly
than by appealing as in 14 to the conclusion of an informal argument
to show there can at most be one maximally consistent states-of-
affairs combination. We can say more simply, relying on the combina-
torial uniqueness of maximal consistency and its implications for the
combinatorial uniqueness of the actual world, that, logically necessar-
ily, the actual world is uniquely actual. We now demonstrate that:
The actual world is uniquely actual:
21. ~œw
i
[Aw
i
÷ Aw
i
] Tautology
22. ~œw
i
[Aw
i
÷ Aw
@
] (15, 21 @-Nominalization)
23. ~œw
i
[Aw
i
÷ w
i
= w
@
] (22)
Actuality defined as maximal consistency combinatorially guaran-
tees that logically something must be actual. There is logically certain
to be some physical being, something rather than nothing. While
necessarily there exists something rather than nothing, what exists is
a matter of pure chance, of combinatorial roulette. If a different
combination had been maximally consistent, a different logically
possible world other than w
@
would exist instead of w
@
, although
whatever logically possible world actually happens to exist could still
be called w
@
. The logical possibility that a combination of states of
affairs and ultimately of objects and properties other than those that
constitute the actual world might have been maximally consistent is
enough to assure that the actual world in all its particularity is logi-
cally contingent.
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 151
Combinatorial pure philosophical ontology
The combinatorial theory of pure philosophical ontology that we
have now developed is not intended as a contribution to applied
scientific ontology. It makes no ontological commitment to any
particular preferred theoretical domain of existent entities, states of
affairs or worlds. All such important discoveries are left to applied
scientific ontology.
To criticize the reduction of ontology to logic misses the mark if it
merely states the obvious but irrelevant fact that logical form lacks
sufficient substantive ontological content to derive a domain of exist-
ent entities. The questions of pure philosophical ontology for which
logic offers insight are conceptual, asking what it means for some-
thing to exist, rather than what actually exists. We should not
conclude that logic cannot offer the required explanation just because
we cannot conjure an actually existent bunny, or even a theoretical
commitment to its existence, wriggling out of a logical magician’s silk
hat. Logic, of course, can do no such thing. The objection misfires by
assuming that a reduction of ontology to logical form is supposed to
provide answers to problems of applied scientific ontology by deriv-
ing a preferred existence domain of actually existent entities. The
possibilities of logical form, on the contrary, are intended instead to
answer another very different specific question about the nature of
being or meaning of existence in pure philosophical ontology consid-
ered exclusively as a discipline.
To avoid equivocation, we proceed carefully, distinguishing the
questions and answers appropriate to divisions among the four mean-
ings of ontology, avoiding conclusions that stand in cross-categorial
purposes to its distinctions. If and when we answer the problems of
pure philosophical ontology, we are entitled to move on to the task of
identifying a preferred existence domain as the goal of applied
scientific ontology. If we do our work well, then the preferred exist-
ence domain we recommend on paper as a result of our theoretical
deliberations will also be the extant domain consisting of the actual
world and all actually existent entities. We produce a system of
categories of existent entities adequate to explain the meaning of
thought and discourse. We then commit applied scientific ontology as
a discipline to a particular applied scientific domain, the theoretical
content of which should ideally correspond perfectly to the real
extant order of existent entities. Logic assumes a secondary role in
applied ontology as a discipline. It is useful in developing a correct
criterion of ontological commitment, and as a watchdog supervising
the inferences we make in trying to establish a preferred theoretical
152 ONTOLOGY
existence domain, particularly with regard to the cardinality of
infinitary and transinfinitary logical domains. Yet it does not decide
any more interesting substantive questions of applied scientific
ontology.
Why is there something rather than nothing? Why is there only
one actual world? If the reason is supposed to be logical rather than
experiential, is the actual world itself logically necessary or logically
contingent? If abstract objects and relations are indistinguishably the
same for every logically possible world, and if we can distinguish logi-
cally possible worlds only as distinct totalities of physical states of
affairs, are the actual physical states of affairs that characterize the
actual world logically necessary or logically contingent? These
questions are not purely academic. If events in the actual world are
logically necessary, as some philosophers have believed, then it
becomes a problem to uphold common-sense belief in free will, free-
dom of action and moral responsibility.
The presupposition of logic that we can predicate properties to
objects makes it intelligible to refer to predication subjects and the
properties predicated of them, without which there would be no
philosophical problem of their ontological status. We can at least
provisionally speak of objects as possible predication subjects and the
properties predicated of them, by virtue of which the problem of the
ontology of objects and properties makes sense. When an object,
whatever an object is and whether or not it exists, whether it is or is
not something more than a logical predication subject, has a property,
whatever a property is and whether or not properties exist, then the
object’s having a property is a state of affairs, while a logically possible
world, including the actual world, and even a logically impossible
model, is constituted by states of affairs, ultimately by objects having
properties. We have used this minimalist logical vocabulary to gain
footing among the difficult questions of pure philosophical ontology.
We reserve until afterwards, when it is appropriate at last to address
the problems of applied scientific ontology, to consider the ontic
status of objects and specific types of objects and properties, states of
affairs and non-actual merely logically possible worlds.
We have argued that to exist is to be maximally consistent. The
combinatorial analysis of the concept of being implies that there is
something rather than nothing because in the ontically neutral predi-
cation sense there must be a maximally consistent combination of
logical objects with properties. We have said that combinatorially
there must be variations among the physical states in distinct logically
possible worlds, and that the actual world is logically contingent
CONCEPTS OF EXI STENCE I N PHI L OSOPHI CAL L OGI C 153
because all physical states of the actual world are logically contingent.
Pure philosophical ontology has now done its job, and can hand over
its analysis of the concept of being for use in applied scientific ontol-
ogy. The existence of physical states of affairs and the potential
convenience of referring to abstract entities, including logical objects
and properties, logical states of affairs, and the like, as candidate items
to include in a preferred existence domain, provide an obvious bridge
to the ontic sciences. We are ready to begin applying the answer to the
question of being, to the analysis of the concept of being as maximal
consistency which we have proposed, to some of the most interesting
specialized fields of applied scientific ontology.
Applied ontology and the
II metaphysics of science
Ontological commitment
6 (on Quine)
A syntactical criterion
To be ontologically committed is to accept the existence of an entity
or type or kind or category of entities. As individual thinkers we make
ontological commitments to the things we believe exist, while theo-
ries in the abstract are ontologically committed to whatever entities
would need to exist in order for the theories to be true.
The first task of applied ontology is to establish adequate criteria of
ontological commitment. Without these we will not be able to certify
a preferred existence domain, as an applied ontology must, because
we will not be able to distinguish one existence domain from another.
We further need such criteria in order to identify the respective onto-
logical commitments of competing scientific theories, especially when
theory choice is supposed to be guided by considerations of explana-
tory economy, and where the search for a preferred existence domain
is conditioned at least in part by the choice of a preferred science.
In “On What There Is”, W. V. O. Quine offers a syntactical criterion
of ontological commitment. We are required to translate a theory such
as Copernicus’s astronomy or Darwin’s biology into a canonical nota-
tion in first-order predicate logic, and then determine the domain of
objects corresponding to each quantifier-bound variable in the
translation that must exist in order for the propositions of the theory
to be true. The idea of Quine’s syntactical criterion is to begin with a
theory that says, in effect, there are chromosomes or there are
unicorns, whose ontological commitments are to be determined. We
first translate these commitment sentences into a canonical notation
like that of standard first-order symbolic logic, to obtain, respectively:
›xCx and ›xUx. The theories are then said to be ontologically
committed to whatever entities must belong to the extensions of
predicates “C” and “U” in order for the sentences of the theories to be
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 157
true. The syntactical criterion of ontological commitment is summa-
rized in Quine’s slogan that “To be is to be the value of a [quantifier-
bound] variable” – a formula in which the ambiguity between being in
the existence and predication senses is explicit.
A theory like that of chromosomes or unicorns is true or false
depending, among other things, on whether or not the ontological
commitments of the theory are included in what we have called the
extant domain of actually existent entities. (The theory must not only
be ontologically committed to actually existent entities, but it must say
only true things about, or truly predicate properties of, these entities.)
Quine further adopts a metaphilosophical position that he calls onto-
logical relativism, according to which we can never attain a perfectly
objective theory-independent overview of all ontic choices. He argues
that as ontologists we enter a competition in which we try to determine
a correct ontology already laden with ontic baggage that can affect even
the interpretation and understanding of another theory’s ontology, as
it influences our judgement about whether this or that ontological
commitment is correct, whether a proposed theoretical existence
domain is coextensive with the relevant extant subdomain.
This alone, paradoxically, should be enough to discredit the
bound-variable criterion of ontological commitment. We are required
to check the bound variables of correctly canonically formalized theo-
ries and interpret the values of the variables as a theory’s ontological
commitment. The first step in Quine’s syntactical criterion appears
easy and obvious. We begin by translating a theory into canonical
logical notation. If ontological relativity prevails, however, as Quine
admits, then his syntactical criterion encounters serious difficulties
right at the outset. We are bound to distort the ontological commit-
ments of a theory that is sufficiently different from our own, espe-
cially if the theory has an interestingly different metaphysics that
cannot be adequately formalized in a Quinean logic. If a theory whose
ontological commitments are to be determined is truly unlike our
own, then we will not be able to rightly recognize it as such by Quine’s
criterion. We cannot decide, in that case, how to translate a radically
ontologically different theory into a canonical bound-variable logical
notation, because for such a theory we cannot know what is or is not
supposed to be a logically possible object and what is or is not
supposed to be a logically possible property.
1
If Quine’s criterion
remains the best that we can do, then we may simply have to live
within its limitations, despite knowing in advance that it is sure to be
a crude instrument for judging the ontological commitments of
ontically remote theories.
158 ONTOLOGY
Pure and applied ontology in Quine
Quine’s oft-quoted opening remarks in “On What There Is” appear
irrefutably commonsensical, but actually embody a confusion about
the tasks of pure and applied ontology. Quine declares:
A curious thing about the ontological problem is its simplicity. It
can be put in three Anglo-Saxon monosyllables: “What is there?”
It can be answered, moreover, in a word – “Everything” – and
everyone will accept this answer as true. However, this is merely
to say that there is what there is. There remains room for disa-
greement over cases; and so the issue has stayed alive down the
centuries.
2
Quine’s question, “What is there?”, seems to require an applied
scientific ontological answer. Perhaps there are physical entities;
perhaps there are abstract entities of particular sorts. We must be
prepared to dispute efforts to specify a preferred existence domain
offered from distinct philosophical perspectives. In contrast, the
answer Quine half-seriously gives, “Everything”, is a more appropri-
ate type of reply to be tendered in pure philosophical ontology. For
Quine, the “everything” that exists is understood extensionally as
incorporating everything in applied scientific ontology in the sense of
the preferred actually extant existence domain of real existent
entities. When he answers the ontological question by saying that
everything exists, he evidently means something rather uninforma-
tive: that every entity, every existent thing, exists. A superficial agree-
ment concerning only the form of the reply is assumed, inviting
disagreement over cases as to the details of content in answering ques-
tions about what there is.
Quine presents a syntactical criterion of ontological commitment
that depends on an extensional interpretation of the quantifiers in the
canonical notation of first-order symbolic logic and its natural
language equivalents. The essential passages in which Quine articu-
lates the criterion begin with these remarks:
We commit ourselves to an ontology containing numbers when
we say there are prime numbers larger than a million; we commit
ourselves to an ontology containing centaurs when we say there
are centaurs; and we commit ourselves to an ontology containing
Pegasus when we say Pegasus is. But we do not commit ourselves
to an ontology containing Pegasus or the author of Waverly or the
round square cupola on Berkeley College when we say that
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 159
Pegasus or the author of Waverly or the cupola in question is not.
We need no longer labor under the delusion that the meaningful-
ness of a statement containing a singular term presupposes an
entity named by the term. A singular term need not name to be
significant.
3
Quine paves the way for the bound-variable criterion of ontologi-
cal commitment by identifying its equivalent in ordinary language.
We commit ourselves ontologically to the existence of a certain entity
or type of entity when we say sincerely and assertorically, even if
falsely, that such a thing or type of thing exists. There is a large variety
of colloquial devices for expressing ontological commitments, which
Quine associates with the use of pronouns such as “he”, “she” and
“it”, all of which are formally expressed by means of quantifier bound
variables, like the “x” in (›x)Fx, which is usually informally inter-
preted as saying, “There is or there exists an entity x, such that x – it,
pronomially – has property F”. Quine adds:
To be assumed as an entity is, purely and simply, to be reckoned as
the value of a variable. In terms of the categories of traditional
grammar, this amounts roughly to saying that to be is to be in the
range of reference of a pronoun. Pronouns are the basic media of
reference; nouns might better have been named propronouns.
The variables of quantification, “something”, “nothing”, “every-
thing”, range over our whole ontology, whatever it may be; and
we are convicted of a particular ontological presupposition if,
and only if, the alleged presupposition has to be reckoned among
the entities over which our variables range in order to render one
of our affirmations true.
4
The syntactical criterion is explicated in terms Quine has widely
popularized in philosophical logic and ontology:
I have argued that the sort of ontology we adopt can be conse-
quential – notably in connection with mathematics, although this
is only an example. Now how are we to adjudicate among rival
ontologies? Certainly the answer is not provided by the seman-
tical formula “To be is to be the value of a variable”; this formula
serves rather, conversely, in testing the conformity of a given
remark or doctrine to a prior ontological standard. We look to
bound variables in connection with ontology not in order to
know what there is, but in order to know what a given remark or
160 ONTOLOGY
doctrine, ours or someone else’s, says there is; and this much is
quite properly a problem involving language. But what there is is
another question.
5
The bound-variable criterion, Quine is clear, does not determine
what actually exists. By itself, it does not provide a factual inventory
of the extant domain of actually existent entities, which only a true
and complete theory of the world or complete conjunction of all true
theories can supply. The syntactical criterion instead provides a way
of establishing the ontological commitments of a given theory in the
sense of the theoretical existence domain needed for the propositions
of the theory to be true. Conditionally, so to speak, if the theory in
competition with all of the alternatives should turn out to be true,
then these values of quantifier variables will be among the actually
existent entities.
The syntactical criterion of ontological commitment works well
enough in many applications, but also suffers from disabling limita-
tions. In his philosophical logic and semantics, Quine is ontologically
committed to a metalinguistic extensionalist semantics by which only
tautologies and sentences expressing predications of constitutive
properties to actually existent entities are true. It might appear that
this is not a serious obstacle to the syntactical criterion, since it speaks
only to the question of whether a particular theory is actually true,
whatever specific ontological commitments the theory happens to
make. The problem is deeper, as we shall see, because it affects
Quine’s interpretation of quantifiers even in assessing the conditional
ontological commitments of conditionally true theories.
Although Quine rightly tries to detach his bound-variable criterion
of ontological commitment from the issue in our terminology of the
extant domain of actually existent entities, he allows the predications
of properties to putative entities to be true only by presupposing the
possibility of referring to the entities belonging to the extant domain.
In contrast, I doubt that we can make much progress in applied scien-
tific ontology without allowing quantifiers to range freely over
entities that belong to a preferred existence domain in the theoretical
sense, meeting frequently with putative intended entities that do not
actually exist and are not actually members of the extant domain. We
cannot apply Quine’s syntactical bound-variable criterion of onto-
logical commitment to reach correct conclusions about the distinct
theoretical preferred existence domains of ontologically incompatible
applied scientific ontologies, or of the scientific or other fields of
thought or discourse that require or presuppose such domains, if, as
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 161
Quine requires, quantifier semantics refer only to the extant domain
of real existent entities, whichever ones they are, in the actual world.
The fault lies not with Quine’s bound-variable criterion considered in
itself, but in the criterion taken together with the extensionalist
semantics that, for Quine, is inseparable from a correct theory of
meaning.
Critique of Quine’s criterion
The underlying problem for Quine’s criterion is that it conflates the
interpretation of quantifier-bound variables in pure logic with those
required by an applied logic in formalizing the principles of a science.
What is wanted instead is ontic neutrality in the logical representation
of scientific theories and philosophical discourse about their respec-
tive ontological commitments. The desired ontic neutrality is
precisely what cannot be maintained on Quine’s bound-variable cri-
terion, given his extensional quantifier semantics.
If the variables bound by existential quantifiers in the formaliza-
tion of a theory are logical objects with no specific ontological com-
mitments, as we have proposed in combinatorial pure philosophical
ontology, then we attain the necessary ontological neutrality to
identify the distinct ontological commitments of different theories
and can compare them as impartially as possible. Quine’s deeply
ingrained extensionalism unfortunately prevents him from acknowl-
edging logical objects in the sense we have prescribed. It entails that a
logical formula formalizing a proposition of a theory cannot be mean-
ingful unless the objects and states of affairs to which it is onto-
logically committed happen actually to exist. A Quinean, as a conse-
quence, cannot intelligibly translate the propositions of alternative
false theories that ostensibly make false ontological commitments to
objects that do not actually exist. The theories themselves can still be
distinguished by exercising what Quine calls semantic ascent, talking
about the language and terminology of the theories rather than about
the actually nonexistent objects to which the theories ostensibly
refer.
6
If theory T says that there are unicorns and theory T* says that
there are centaurs, then extensionally the theories have indistinguish-
able ontologies, both alike being ontologically committed to the null
or empty domain, on the assumption that neither unicorns nor
centaurs happen to exist.
7
That inevitable confusion of distinct onto-
logical commitments in itself is a problem for Quine, but it is only a
symptom of worse difficulties. Why, we must ask, should the effec-
tiveness of a criterion of ontological commitment depend on the
162 ONTOLOGY
contingent facts of the actual world that happen only by pure chance
to include zebras and giraffes but no mermaids, unicorns or centaurs?
To make the criterion function properly, Quine contra Quine
would need to trade-in his extensionalist quantifier semantics for an
ontologically neutral reference to logical objects and properties.
Quine nevertheless understands the project of scientific semantics in
much the same way as Gottlob Frege, interpreting reference and true
predications of properties exclusively in terms of actually existent
entities.
8
This, to put it mildly, makes it awkward, and in the end not
very satisfactory, to understand the meaning and ontological commit-
ments of theories that turn out, as a sheer matter of logically contin-
gent fact, to be false by virtue of their ontological commitments to
theoretical existence domains that are not included in what we believe
to be the extant domain of actually existent entities.
Quine seems to recognize the need for ontic neutrality at some
level in applying his criterion. His strategy for disposing meta-
linguistically of terms in a language that require reference to actually
existent entities derives from Russell’s three-part extensionalist analy-
sis of definite descriptions.
9
Where Russell breaks down a sentence of
the form “The F is G” into “There exists at least one F, there exists at
most one F, and that thing is or has property G”, Quine applies the
same existence-presuppositional analysis to avoid the necessity of
interpreting sentences containing definite descriptions or names as
disguised definite descriptions exhibiting “objective reference” to
actually existent entities in the extant domain. Quine introduces two
imaginary characters, McX, a realist in metaphysics who incautiously
accepts the existence of entities in order to make sense even of true
pronouncements of their nonexistence, and his phonetically comple-
mentary fellow traveller, Wyman, who tries to explain the semantics
of non-being without allowing reference to nonexistents by admitting
the existence of unactualized possibles. Quine condemns both
approaches, and holds that neither strategy is needed in light of an
analysis of the meaning of sentences making ostensible reference to
beingless objects. Quine maintains:
The unanalyzed statement “The author of Waverly was a poet”
contains a part, “the author of Waverly”, which is wrongly
supposed by McX and Wyman to demand objective reference in
order to be meaningful at all. But in Russell’s translation, “Some-
thing wrote Waverly and was a poet and nothing else wrote
Waverly”, the burden of objective reference which had been put
upon the descriptive phrase is now taken over by words of the
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 163
kind that logicians call bound variables, variables of quantifica-
tion, namely, words like “something”, “nothing”, “everything”.
These words, far from purporting to be names specifically of the
author of Waverly, do not purport to be names at all; they refer to
entities generally, with a kind of studied ambiguity peculiar to
themselves. These quantificational words or bound variables are,
of course a basic part of language, and their meaningfulness, at
least in context, is not to be challenged. But their meaningfulness
in no way presupposes there being either the author of Waverly or
the round square cupola on Berkeley College or any other specifi-
cally preassigned objects.
10
It is quantifiers to the rescue, as by now we should expect. Yet
things are not as straightforward as Quine suggests. The reason is that
quantifiers themselves are interpreted extensionally by Quine as rang-
ing over the extant domain of actually existent entities, thereby
making the Russell–Quine-style analysed sentence “Something wrote
Waverly and was a poet and nothing else wrote Waverly”, every bit as
ontologically loaded as the original unanalysed sentence “The author
of Waverly was a poet”. How, indeed, could the situation be otherwise
if the Russell–Quine paraphrase purports to be an analysis of the
meaning of the original sentence? The analysis would be defective if,
in substituting the bound-variable formula for the proper name
expression, it let this vital determinant of the sentence’s meaning slip
through its fingers.
The further crucial question that is not settled by Quine’s endorse-
ment of Russell’s method is whether in the first place the analysis is
correct. The omission is clearly problematic, particularly in the
context of trying to establish the ontological commitments of compet-
ing theories. The chief difficulty is that on Russell’s and Quine’s
extensional theories of meaning, only actually existent entities actu-
ally have properties, while nonentities do not. It is infamous, for
example, that on Russell’s analysis of definite descriptions the
sentences “The winged horse is winged” or “The winged horse has
wings” and “The winged horse is a horse” are all false, because in the
extant domain of actually existent entities there contingently exist no
winged horses. Such an unreflectively extensionalist conclusion is
inimical to the intensionalist combinatorial analysis of being as maxi-
mal consistency. The combinatorial theory entails that nonexistent
entities considered only as logical objects as truly have the properties
by which they are constituted as do the actually existent entities that
happen to populate the actual world.
164 ONTOLOGY
Nor is this merely a conflict between the combinatorial analysis
versus Russell’s and Quine’s analysis of definite descriptions. Intui-
tively, it seems correct to say that the winged horse is winged and a
horse, even though no winged horse actually exists. That, it might
reasonably be said, is precisely why the winged horse does not exist,
because the properties it has, that are truly attributed to it, are not
manifested by any actually existent winged or equine entity. If the
winged horse does not fail to exist because its property combination,
although containing at least the properties of being winged and a
horse, is otherwise predicationally incomplete despite being consist-
ent, then what is the explanation of its nonexistence? If the nonexist-
ence of the winged horse is merely the fact that the actual world does
not happen to contain a horse with wings, then we have only restated
the fact of the winged horse’s nonexistence, and not taken any steps
toward explaining the fact. We have not, in that case, undertaken to
clarify what it means for the winged horse not to exist, or for the
actual world contingently not to contain a winged horse in the extant
domain of actually existent entities.
Quine claims that the descriptive fragment “the author of Waverly”
in the sentence “The author of Waverly was a poet” does not need to
carry objective reference in order to be meaningful. This is true only
in the limited sense according to which Quine is willing to unpack the
meaning of the sentence in terms of Russell’s theory of definite
descriptions. He rightly observes that the “objective reference” of the
term, analysed or unanalysed, does not disappear under analysis, but
is instead taken up by an existential quantifier of appropriate scope
within the analysis and by the same range of “objective” entities.
These are not just the putative entities that are recommended in a
preferred theoretical existence domain, but the actually existent enti-
ties of the extant domain. It is mystifying, nonetheless, why and by
what philosophical considerations Quine should impose this exten-
sionalist requirement on the meaning of sentences in theories whose
ontological commitment is to be established by the syntactical bound-
variable criterion, when in the present context he does not try to
specify a “correct” ontology.
11
Quine thereby undermines the impression of achieving any degree
of neutrality in the syntactical criterion of ontological commitment.
He does not go far enough, in the end, when in the passage quoted
above he says only that the “meaningfulness [of the quantifiers] in no
way presupposes there being either the author of Waverly or the
round square cupola on Berkeley College or any other specifically
preassigned objects”. This is true enough, but the meaning of the
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 165
quantifiers is hardly the issue. Where we require ontic neutrality in a
correct criterion of ontological commitment is rather in understand-
ing the existence claims made by false theories involving predications
of null extension that are ostensibly ontologically committed to
things that do not happen to exist. Quine’s qualification is true only
because the meaning of quantifiers in his extensionalist semantics is
fixed relative to the extant domain of actually existent entities. He
does not unpack a sentence about the round square cupola on
Berkeley College as having, say, the property of being round and the
property of being square, a cupola, located somewhere on or at
Berkeley College, and so on. If he did so according to Russell’s three-
part analysis of definite descriptions, then, assuming there exists and
can exist no round square entity, he would obtain only false sentences.
The round square cupola is not round, not square and not a cupola,
and fails necessarily to adorn Berkeley College.
What, then, are we talking about when we utter the phrase “The
round square cupola on Berkeley College”? Are we only jabbering? Do
we speak literally of nothing, just because what we believe ourselves to
be talking about happens not to exist? Or are we talking only about the
words that the sentence contains? Why, then, must the semantic analy-
sis of the meaning of a sentence that happens to be about logically
contingently actually existent entities have to be so different? Why
does a sentence about actually existent entities turn out to be about the
objects it purports to be about and not about the words and phrases by
which the sentence is expressed in a Quinean semantic ascent? If
Quine’s theory of ontological commitment taken together with his
extensionalist quantifier semantics has these implications, and must
answer so implausibly to these reasonable questions, then surely it does
not provide the ontic neutrality required for an adequately impartial
interpretation of the ontological commitments of competing theories.
Quine, rightly for this purpose, but inadequately, says that the mean-
ingfulness of a quantifier does not presuppose the existence of any
“specifically preassigned objects”. The meaningfulness of a quantifier
for Quine, in spite of this disclaimer, significantly presupposes that
only actually existent entities can be the values of bound variables, and
that only actually existent entities can possibly be the objects of true
predications of constitutive properties.
To say that “The round square cupola is round and square and a
cupola” is to utter something irredeemably false for Quine. A theory
ontologically committed only to the round square cupola could not
then be said to have anything whatsoever in its preferred existence
domain. That is, paradoxically, that a theory ostensibly ontologically
166 ONTOLOGY
committed only to the round square cupola does not actually have any
ontological commitments, and in particular is not and cannot be
ontologically committed to the existence of the round square cupola.
If it seems too fanciful to suppose that a theory might be ontologically
committed to such an obviously predicationally inconsistent putative
entity, then consider as a more historically seditious example the
recent putative ontological commitments by many of the most
respected logicians, analytic philosophers and mathematicians to the
existence, and even necessary existence, of a reduction of infinitary
arithmetic to the axioms of logic and naive set theory.
12
If, by Quine’s criterion as it now appears, no theory can be
ontologically committed to the existence of the round square cupola,
and if no theory, due to the contingent facts of existence and non-
existence in the actual world, is actually ontologically committed to
the existence of a winged horse or phlogiston or vortices or the æther
or the planet Vulcan or the philosopher’s stone, then in what sense
can the bound-variable criterion be correct? In what sense can
Quine’s criterion deliver an accurate account of the ontological com-
mitments of theories that are ostensibly ontologically committed to
what, from the standpoint of the extant domain of actually existent
entities, are actually nonexistent entities? Quine’s criterion fails the
most basic prerequisite for a method of establishing the ontological
commitment of a theory if it only gives correct results in the case of
theories ontologically committed to the extant domain. It fails
precisely because it is not ontically neutral; its extensionalism does
not meet the demand for ontic neutrality in the interpretation of
quantifiers and bound variables in formalizations of a theory’s pre-
sumed ontological commitment sentences. It limits the specific mean-
ingfulness of such sentences exclusively to the general meaningfulness
of quantifiers. The specific meaning, however, and not merely the
meaningfulness of a theory’s ontologically committal sentences, must
be nailed down in order to establish fine distinctions of ontological
commitment among competing theories.
The result of Quine’s extensional semantics of quantifiers being
dependent on the extant domain of logically contingent actually
existent entities is that the determination of ontological commitment
is restricted exclusively to true theories ontologically committed to the
existence of existent entities, and falls far short in correctly identifying
and representing the ontological commitments of false theories. There
is thus a kind of semantic arrogance built into any extensionally inter-
preted quantifier and bound-variable criterion of ontological commit-
ment that favours not only the pale meaningfulness but the exact
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 167
explicit meaning of sentences in true theories, and distorts when it is not
simply oblivious to the meaning of any false theory.
Understanding ontological disputes
As a consequence of his extensional interpretation of the quantifiers in
logic and natural languages, Quine is equally unable to make intuitively
correct sense of ontological commitment in the case of numbers and
universals. These are the purported entities about which logicians and
philosophers have raised the most ruckus in traditional metaphysics,
exemplified by the realism–nominalism debate that has dominated
applied ontology ever since Plato. Quine wants to represent the distinct
ontological commitments of both sides and every subtle intermediate
theory in this important ontological dispute. He explains:
Up to now I have argued that we can use singular terms
significantly in sentences without presupposing that there are the
entities which those terms purport to name. I have argued further
that we can use general terms, for example, predicates, without
conceding them to be names of abstract entities. I have argued
further that we can view utterances as significant, and as synony-
mous or heteronymous with one another, without countenancing
a realm of entities called meanings. At this point McX begins to
wonder whether there is any limit at all to our ontological immu-
nity. Does nothing we may say commit us to the assumption of
universals or other entities which we may find unwelcome?
I have already suggested a negative answer to this question, in
speaking of bound variables, or variables of quantification, in
connection with Russell’s theory of descriptions. We can very
easily involve ourselves in ontological commitments by saying,
for example, that there is something (bound variable) which red
houses and sunsets have in common; or that there is something
which is a prime number larger than a million. But this is, essen-
tially, the only way we can involve ourselves in ontological
commitments: by our use of bound variables. The use of alleged
names is no criterion, for we can repudiate their namehood at the
drop of a hat unless the assumption of a corresponding entity can
be spotted in the things we affirm in terms of bound variables.
Names are, in fact, altogether immaterial to the ontological issue,
for I have shown, in connection with “Pegasus” and “pegasize”,
that names can be converted to descriptions, and Russell has
shown that descriptions can be eliminated.
13
168 ONTOLOGY
In this expanded version of his previous argument, Quine imagines
an applied ontologist who makes an ontological commitment to the
existence of a certain universal, red or redness, and a certain prime
number. If the extant domain should turn out not to contain these
putative abstract entities, then no theory on Quine’s bound-variable
criterion of ontological commitment with its extensionalist interpre-
tation of the quantifiers can actually be ontologically committed to
red or redness or any prime number. We do not, in fact, contrary to
Quine’s assertion, ontologically commit ourselves in that case to
abstract entities by saying that “there is something that red houses and
sunsets have in common”, or that “there is something that is a prime
number larger than a million”. If there are no universals and no
numbers, then no theories on Quine’s criterion interpreted exten-
sionally, as Quine requires, are committed to such things because
there are no such things, no objects (contrary to McX), even merely
logically possible objects (contrary to Wyman), that actually possess
the properties in question, to which a theory can be committed.
It is incomprehensible in light of the limitations of an extensional
interpretation of quantifiers and bound variables in quantified formu-
lations of ontological commitment sentences to suppose that a syntac-
tical criterion can possibly do justice to the ontological commitments
of false theories ostensibly ontologically committed to entities that
necessarily or per chance do not happen to belong to the extant domain
of actually existent entities. Despite this evident limitation, Quine per-
sists in maintaining the opposite, as though his criterion treated the
ontological commitments of all theories fairly and alike, when he adds:
This, I think, is characteristic of metaphysics, or at least of that
part of metaphysics called ontology: one who regards a statement
on this subject as true at all must regard it as trivially true. One’s
ontology is basic to the conceptual scheme by which he interprets
all experiences, even the most commonplace ones. Judged within
some particular conceptual scheme – and how else is judgment
possible? – an ontological statement goes without saying, stand-
ing in need of no separate justification at all. Ontological state-
ments follow immediately from all manner of casual statements
of commonplace fact, just as – from the point of view, anyway, of
McX’s conceptual scheme – “There is an attribute” follows from
“There are red houses, red roses, red sunsets”.
14
Quine boxes himself in by insisting on the ontological relativity of
ontological investigations, reinforced by his thesis of the indeterminacy
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 169
of radical translation. If I cannot know in any meaningful way whether
a tribesman I encounter as a field linguist means, by “Gavagai”, “Lo,
a rabbit”, or, “Lo, a sequence of undetached rabbit parts”, how can I
hope to know what a scientist who might not exactly share my onto-
logical commitments means by speaking of “mass”, “force”, “cause” or
“momentum”? If, indeed, I cannot penetrate these referential opacities,
how can I possibly hope to formalize such discourse in the canonical
logical symbolism of first-order logic in order to ascertain the theory’s
ontological commitments by applying the bound-variable criterion?
What could such a theory’s predicates mean to me if the ontology and
conceptual scheme that are built into my language are so different?
How can I decide whether the theory in question is more correctly
formalized in terms of predicates or names or indexicals or descriptions
or something altogether unfamiliar to the logic at my disposal?
15
The syntactical criterion of ontological commitment, by Quine’s
reasoning, is not a perfectly ontically neutral instrument for discover-
ing a theory’s ontological commitments. It works properly in identify-
ing ontological commitments only for theories that can be accurately
formalized in an already ontically loaded canonical predicate–quantifier
notation, and then only in application to theories that happen to make
true ontological commitments. That is to say, ironically, that Quine’s
criterion is subjectively limited by what a user of the method believes
to be the extant domain. There is no reason to think, and, in light of
Quine’s theory of ontological relativity, substantial reason not to
believe, that there cannot be thinkers and language users whose ontic
framework is radically unlike that of an extensionalist who agrees with
Quine about the contents of the preferred existence domain, implicitly
assumed by the criterion to be identical with the extant domain. Quine’s
criterion either imposes the user’s ontic categories and ontological
commitments on every theory it attempts to judge, or else it must
syncretically include all logical notations indiscriminately, regardless of
their syntactical compatibility or incompatibility.
Do we know in advance whether we might ever need to use quan-
tified modal logic to represent the propositions of a theory whose
ontological commitments are supposed to be judged by Quine’s cri-
terion, but that are opposed in interesting ways to Quine’s own onto-
logical commitments? Quine resisted quantified modal logic through
much of his career, although he seems later to have softened his philo-
sophical objections. If we exclude quantified modal logic from the
syntactical criterion’s canonical notation, how can we possibly do
justice to the ontological commitments of an alien theory of quanti-
fied modal logic? Should we ignore it because we “know” that it is
170 ONTOLOGY
false or unsound or deductively unclosed? How do we know that it
suffers from any of these logical defects if we cannot first accurately
determine its ontological commitments? A correct criterion of
ontological commitment must do equally ontically neutral double
duty in evaluating the ontological commitments of true and false
theories alike.
Quine’s objection to quantified modal logic is independent of its
ontological commitments. Quine does not rule quantified modal logic
out of the canonical notation because he objects to its ontology. He
resists quantified modal logic because he believes such systems are
intensional, because they do not permit the intersubstitution of
coreferential terms or logically equivalent sentences salva veritate,
and because he believes that logic and the semantics of logic must be
purely extensional. Otherwise, he thinks we risk psychologism that
results when we try to make logic into something conceptual and
subjective. Quine’s reasoning in rejecting quantified modal logic can
be disputed at every step. The argument to show that quantified
modal logic is intensional is not particularly convincing. Quine
considers an inference from the true assumptions that ~(9 > 7) and
the number of planets = 9, to the presumably false conclusion, substi-
tuting identicals in the second assumption within the modal context
of the first assumption, that ~(the number of planets > 7).
16
The
problem is that the substitution is unjustified if the assumption that
the number of planets = 9 is paraphrased without loss of meaning as
a predication rather than a literal statement of numerical identity.
What, after all, does pure mathematics know about planets? The
assumption might be more accurately entered into a canonical logical
notation, not as an identity statement, but as a predication, in which
the planets are said to have the property of being nine-fold in number,
from which no identity substitutions within or without modal con-
texts are deductively authorized.
17
The point remains that if Quine considers it philosophically
permissible to exclude a formalism like quantified modal logic from
the canonical notation required by the syntactical criterion of onto-
logical commitment, then the criterion does not apply to and cannot
be used accurately to determine the ontological commitments of
excluded theories. Quine’s reason for discounting quantified modal
logic is his belief that it is intensional. Even and especially if his argu-
ment is correct, and we have argued the contrary, he thereby excludes
all intensional theories from proper determination of their radically
different ontological commitments by means of the quantifier bound-
variable criterion. Is the syntactical criterion unable to judge correctly
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 171
the ontological commitments of any intensional theory? To exclude
intensional theories from the bound-variable criterion is to exercise
subjective choice in establishing the ontological commitments of
other theories. By maintaining a tight rein on the syntactical cri-
terion’s canonical notation, Quine unnecessarily limits its applicabil-
ity. If he loosens his grip and allows other notations to be added
indiscriminately to the canon, then he can no longer keep ontology in
the sense of his philosophically preferred existence domain as austere
in its ontological commitments as he would like.
An intensionalist using an intensional but, from an intensionalist
perspective, equally legitimate deservedly canonical notation, rather
than Quine’s extensional notation, is sure to produce a different char-
acterization than Quine’s of the ontological commitments of the same
theories. All this indicates, not that intensionalism is preferable to
extensionalism, although we might finally arrive at this conclusion,
but that a good criterion of ontological commitment ought to identify
the ontological commitments of even those radically opposed general
categories of theories, which, regardless of whether they are correct
or incorrect, can only be so judged on the basis of their respective
correctly specified ontological commitments. The objection implies
that it is mistaken for both intensionalists and extensionalists to apply
any criterion like Quine’s if it is limited to the syntactical properties of
any chosen logic or language for expressing a theory’s principles.
What is wrongheaded about the syntactical criterion is its idea that an
already philosophically privileged syntax can be used fairly and accu-
rately to represent the propositions of any other arbitrary theory. Any
notation inevitably imposes a choice of prior ontological commit-
ments on the theories it is used to formalize. The conservative
exclusionary attitude towards canonical syntax required by Quine’s
criterion makes every determination of ontological commitment
ontically biased.
It would, on the other hand, be logically chaotic to allow the
canonical notation of Quine’s criterion syncretically to incorporate
all logical notations for the sake of being able more sympathetically to
translate the commitment sentences of any theory. There is nothing
canonical about a notation if it lets in all the formalisms that would
otherwise be excluded from the syntactical criterion. Which logic are
we supposed to use in a particular application when the notations are
all jumbled together? Are we meant to use only the logical notation of
theory T in investigating the ontological commitments of T by
Quine’s criterion? Or do we also have the option or even the respon-
sibility to test T by translating it into every distinct logical notation
172 ONTOLOGY
indiscriminately brought into the canon? What are we to make of
conflicting ontological commitment judgements that must arise if we
can apply the bound-variable criterion to the formalization of a theo-
ry’s commitment sentences in any and every logical notation? If we
open the door to additional logical symbolisms, say, the notation and
formal semantics of quantified modal logic, including those that
Quine regards as non-canonical, then we must presumably let them all
in, on pain of landing again on the first dilemma horn. We shall then
inevitably lack adequate syntactical resources to formalize or collo-
quially paraphrase the ontological commitment sentences of all theo-
ries so as to be able to apply the bound-variable criterion in trying to
identify their ontological commitments.
If these were Quine’s only choices, then he might be expected to
decide in favour of the logically more manageable alternative. The
syntactical criterion with a conservative canonical notation still comes
at the heavy price of applying only to those theories whose ontologi-
cal commitments are accurately expressible in Quine’s exclusionary
canonical notation. The notation Quine has in mind is undoubtedly
meant to be a version of A. N. Whitehead and Russell’s predicate
syntax in Principia Mathematica, supplemented and refined as neces-
sary in response to advances in mathematics, or equivalently perhaps
a corrected version of Quine’s “New Foundations for Mathematical
Logic”.
18
Even so, the restriction remains too severe. How is Quine’s
criterion rightly to evaluate the ontological commitments of theories
whose logics are radically different from the extensionalist canon?
Nor does Quine try to show that intensional logic must introduce
havoc if it merged with a more classical extensional logic. There are
intensional logics that are formally as interesting as their extensional
counterparts, and that know how to behave themselves in polite
extensional company. Although allowing such an exception, as the
second part of our dilemma suggests, opens up more possibilities for
accurately identifying the ontological commitments of more distinct
kinds of theories, it could also be the highly objectionable thin edge of
the wedge leading to an unrestricted incoherent accumulation of any
and all logical symbolisms in the criterion’s expanded “canonical”
notation.
Limitations of Ockham’s razor in applied ontology
In his preference for austere desert landscapes over lush tropical
ontologies, Quine champions the use of Ockham’s razor in applied
scientific ontology. This fact makes the logic and methodology of his
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 173
theory of ontological commitment especially problematic. Quine
ultimately maintains that, adopting the bound-variable criterion of
ontological commitment and working toward our own decisions
about what scientific theories and applied ontologies to accept, we are
ontologically committed to whatever entities must be assumed to
exist as the values of object variables bound by existential quantifiers
in the canonical first-order logical formalization of favoured theories
in order for the principles of the theory to be true.
Quine prefers minimalist existence domains, the very least we need
to get by in mathematics and science. Ultimately, Quine argues that
applied scientific ontology needs to include both individual physical
entities and abstract classes. Quine believes that numbers in the foun-
dations of mathematics and ostensible references to universals,
propositions and other putative abstract entities, in so far as they are
needed in mathematics, science and philosophy, can be ontologically
reduced to classes, and that, in the absence of classes, we too severely
curtail ontology for the purposes of mathematics and science. We
need classes as abstract entities in ontology because we cannot do
without them, and only for that reason does Quine grudgingly admit
that they exist. Were it otherwise, if we could understand mathemat-
ics and science without including abstract classes in the ontology, then
Quine, having tried the experiment and failed, would conclude they
could and therefore should be said not to exist. Quine’s ontological
minimalism is in many ways attractive, not least because in slinging
Ockham’s razor to exclude as nonexistent ostensible entities for
which there is no demonstrated theoretical need, we restrict the
possibilities of inadvisable ontological commitments to entia
suspecta, in subdivisions of applied ontology that are not subject to
verification by empirical observation. Their exclusion notably incor-
porates the category of ostensible abstract entities to which many less
scientific metaphysical systems have sometimes been committed and
inclined to accept as real existent entities in a lavishly appointed
Platonic heaven.
19
The trouble is that by applying Ockham’s razor in this way we risk
slipping into the methodological circle that obtains when we try to
choose among alternative theories on the basis of their ontologies, and
try to establish their advantages and weigh them against the disadvant-
ages of alternative ontologies on the basis of a preferred choice of
theories. We need to know what sciences and kinds of sciences to
promote in order to decide what entities are strictly needed or that
would be explanatorily superfluous in a preferred applied scientific
ontology, and we need to know how to choose among the alternative
174 ONTOLOGY
ontological commitments of distinct theories in order to decide which
sciences or kinds of sciences to promote. This is a more serious prob-
lem than is generally recognized in Quine’s writings or in the second-
ary literature on Quine’s philosophy. The difficulty becomes acute
when we try to apply Quine’s criterion to a serious dispute of ontologi-
cal conflict, such as the problem of universals. Quine argues:
Now let us turn to the ontological problem of universals: the
question whether there are such entities as attributes, relations,
classes, numbers, functions. McX, characteristically enough,
thinks there are. Speaking of attributes, he says: “There are red
houses, red roses, red sunsets; this much is prephilosophical com-
mon sense in which we must all agree. These houses, roses, and
sunsets, then, have something in common; and this which they
have in common is all I mean by the attribute of redness.”
20
Similar observations are offered in the case of putative mathemati-
cal entities. Quine nowhere acknowledges the difficulty of making
sense of ostensible ontological commitments to nonexistent merely
putative entities on an extensionalist interpretation of quantifier
bound variables. Instead, he reports:
Classical mathematics, as the example of primes larger than a
million clearly illustrates, is up to its neck in commitments to an
ontology of abstract entities. Thus it is that the great mediaeval
controversy over universals has flared up anew in the modern
philosophy of mathematics. The issue is clearer now than of old,
because we now have a more explicit standard whereby to decide
what ontology a given theory or form of discourse is committed
to: a theory is committed to those and only those entities to
which the bound variables of the theory must be capable of refer-
ring in order that the affirmations made in the theory be true.
21
A theory of universals, one would think, is ontologically commit-
ted to the existence of universals. Likewise for a theory of mathemati-
cal entities. If there are no such entities in the extant domain, then for
Quine these false theories are not actually ontologically committed to
anything at all. A theory is ontologically committed to those and only
those entities to which the bound variables of the theory must be
capable of referring “in order that the affirmations made in the theory
be true”, Quine says. But which entities are these in the case of a
theory of the winged horse? Not the winged horse, for on an
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 175
extensionalist reading of the quantifiers there is no such thing. No
entity or nonentity truly has the properties of being winged and a
horse on Quine’s extensionalist interpretation of quantifiers. There
is, then, no entity or nonentity to which a theory of the winged horse
can be ontologically committed. The same is true of any theory of
universals or numbers or other putative mathematical entities if they
do not actually exist, whereupon the theories themselves disappear or
are bleached of meaning, and with them the possibility of making
sense of alleged controversies in the history of metaphysics whose
conflicting ontological commitments Quine claims to represent.
Quine is not unaware of the problems of relying on principles of
theoretical simplicity and economy in moving toward a preferred
existence domain. He warns against the uncritical application of these
standards without considering a broader conception of explanatory
usefulness in deciding what is or is not needed in explanation. Thus,
he states:
But simplicity, as a guiding principle in constructing conceptual
schemes, is not a clear and unambiguous idea; and it is quite capa-
ble of presenting a double or multiple standard. Imagine, for
example, that we have devised the most economical set of concepts
adequate to the play-by-play reporting of immediate experience.
The entities under this scheme – the values of bound variables – are,
let us suppose, individual subjective events of sensation or reflec-
tion. We should still find, no doubt, that a physicalistic conceptual
scheme, purporting to talk about external objects, offers great
advantages in simplifying our over-all reports. By bringing together
scattered sense events and treating them as perceptions of one
object, we reduce the complexity of our stream of experience to a
manageable conceptual simplicity. The rule of simplicity is indeed
our guiding maxim in assigning sense data to objects: we associate
an earlier and a later round sensum with the same so-called penny,
or with two different so-called pennies, in obedience to the
demands of maximum simplicity in our total world-picture.
22
It might be possible to have a phenomenalist ontology of sense
impressions only, in the manner of Condillac, Berkeley, Hume or
Ernst Mach.
23
Quine thinks that, despite the simplicity of the account,
it would still be preferable to admit external entities related somehow
to our sensations of them in a more common-sense or naive realist
Aristotelian ontology. Where putative abstract entities are concerned,
on the other hand, Quine generally wields Ockham’s razor to
176 ONTOLOGY
eliminate from his own preferred theoretical existence domain
whatever abstract entities are not absolutely necessary to conduct the
business of mathematics and science. He finds, in the process, that he
cannot do without classes, from which numbers and other mathemati-
cal entities can be constructed, and these, he argues, must therefore
exist.
To the extent that Quine relies on Ockham’s razor, he opens his
criterion of ontological commitment to several kinds of objections.
He proceeds as though we could conjure entities into or out of exist-
ence purely on the grounds of our perceptions of our extracurricular
theoretical needs in the sciences. Such a strategy has two unfortunate
conflicts in Quine’s programme. It snags on the problem of identify-
ing favoured sciences and preferred ontologies, and it runs into the
difficulty of establishing fixed needs in determining which ontologi-
cal commitments do or do not amount to multiplying entities beyond
strict theoretical explanatory necessity.
What are the real needs that are to dictate the contents of a pre-
ferred existence domain for the sciences – assuming that we can some-
how independently decide which among the competing possibilities
we need or want to support – in specifying the details of a preferred
existence domain in applied scientific ontology? The difficulties we
encounter in trying to answer this question satisfactorily reflect on the
doubtful utility of applying Ockham’s razor to decide sensitive issues
about the extant domain. Quine also regards the principle of explana-
tory economy as equivocal. He nevertheless appeals throughout his
work to considerations of minimizing ontological commitment to
what is strictly needed for science, without, remarkably, stopping to
ask how choice of science affects choice of ontology and choice of
ontology influences choice of science. Quine remarks:
Our acceptance of an ontology is, I think, similar in principle to
our acceptance of a scientific theory, say a system of physics: we
adopt, at least insofar as we are reasonable, the simplest concep-
tual scheme into which the disordered fragments of raw experi-
ence can be fitted and arranged. Our ontology is determined once
we have fixed upon the over-all conceptual scheme which is to
accommodate science in the broadest sense; and the considera-
tions which determine a reasonable construction of any part of
that conceptual scheme, for example, the biological or the physi-
cal part, are not different in kind from the considerations which
determine a reasonable construction of the whole. To whatever
extent the adoption of any system of scientific theory may be said
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 177
to be a matter of language, the same – but no more – may be said
of the adoption of an ontology.
24
The full implications, amounting to a vicious methodological
circle, of trying simultaneously to choose a preferred existence
domain as that required by a favoured scientific theory and of choos-
ing a favoured scientific theory (bacteria instead of demons as a cause
of disease; atmospheric electrical accumulation and discharge of
hydrogen ions versus Zeus’s wrath) in terms of its philosophically or
quasi-aesthetically preferable ontological commitments, seems to be
unappreciated by Quine.
Quine cannot presuppose that the domain of existent entities is
already known independently of the philosophically justified prefer-
ence for one existence domain over its competitors. The only way to
arrive at a philosophically justified preference for an existence
domain over its rivals is to apply a correct criterion of ontological
commitment to competing theories in order to decide which to prefer
on grounds of simplicity, economy, theoretical fruitfulness or the like.
There is thus a deep circularity in Quine’s definition of and sugges-
tions for applying his syntactical bound-variable criterion of onto-
logical commitment in the comparative evaluation of competing
existence domains. We are supposed to use the criterion in order to
decide which existence domain to prefer, in choosing whether to
accept a domain that includes or excludes propositions or other
intensional objects, or that includes or excludes sets but not
universals. In order to apply Quine’s criterion that to be is to be the
value of a quantifier-bound variable, we must already know the values
of bound variables, which is to say that we must already be in firm
possession of a preferred existence domain. This again we cannot do
unless or until we have applied Quine’s criterion as a first step in
assessing the advantages and disadvantages of competing existence
domains.
Ockham’s razor by itself cannot determine which theories are true
and which are false. The reason, we should remind ourselves, is that
while there could in principle be as many theories as there are
ontologies, there are in fact for logical as well as practical reasons more
theories than ontologies. There are multiple theories that share the
same ontology while making different jointly logically incompatible
assertions about exactly the same entities. This can obviously be the
case if theory T states that object O is an electron and not a neutron,
and theory T* states that the very same object O is a neutron and not
an electron. The two theories, by hypothesis, are ontologically commit-
178 ONTOLOGY
ted to the existence of object O, and to the existence of at least some,
or to the scientific category of, electrons and neutrons, or to the
extensions of the count nouns or general terms “electrons” and
“neutrons”. Clearly, Ockham’s razor by itself offers nothing positive to
decide which, if either, theory T or T* is true in classifying object O as
electron or neutron in a microphysical taxonomy.
25
There is additionally a problem about correctly discerning the
internal ontological content of any of these expressions on Quine’s
theory. The difficulty arises even in trying to capture the distinctive
ontological commitments of theories about, say, objectified unitary
rabbits and spatiotemporally sequential undetached rabbit parts. If we
cannot accomplish this translation task with any assurance of success,
how can we then go on to assess the merits of each such theory
according to its specific ontological commitments, in order to decide
whether to accept the theory as a part of science by virtue of judging
that it better satisfies the aesthetic requirements of Ockham’s razor
than its competitors? Quine’s ontological project again lapses into
circularity precisely at this juncture, when we reflect that it is the
choice of a preferred science and its particular ontological commit-
ments that in Quine’s view of the insensible grading off of philosophy
into natural science is supposed to play a substantial role in selecting
a preferred existence domain for all of philosophy, logic, mathemat-
ics, and science.
Combinatorial criterion of ontological commitment
It may thus be time to ask whether a syntactical criterion of ontologi-
cal commitment in any form is likely to succeed, or whether we ought
now to begin considering alternatives to syntactical criteria of any type.
There is much to admire in Quine’s work on ontology. Quine sets
applied scientific ontology on the right track, even if the account he
offers requires revision as a whole in order to arrive, first, at a correct
criterion of ontological commitment, and then to put the criterion to
good use in identifying a preferred existence domain with a strong
presumption of its according with the extant domain of actually
existent entities. The counter-proposal to be defended below places
applied scientific ontology on a more definite foundation, based on
the combinatorial answer to the question of being in pure philosophi-
cal ontology, by explaining intensionally what it means for something
to exist in terms of predicational maximal consistency.
The definition of being as maximal consistency can be applied to the
problem of articulating a preferred existence domain. We proceed more
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 179
informally and positively on this crucial front now that we have in hand
a tested definition of the concept of being to fill in the blanks in a
complete account of applied scientific ontology. Let us turn again to
Quine’s trenchant questions. What, first, must I do in accepting a
scientific theory to commit myself ontologically to a physical object like
a chair or a mitochondrion or an electron or the entire physical
universe? What must I do to commit myself ontologically to an abstract
object like a number or set or property, relation, proposition or state of
affairs? What must I do to commit myself ontologically to the existence
of persons or minds, God or the gods, demons, angels or spirits, destiny,
moira or kharma? Quine claims one need only assert “There are chairs”
or “There are mitochondria” or “God exists”. If we choose, we can
write these commitment sentences more perspicuously in a logical
symbolism, from which we can then read off ontological commitments
from the occurrences of bound variables within the scope of existential
quantifiers. We have seen that Quine’s answer is both viciously circular
and counter-intuitive, however, if, with Quine, we also try to interpret
the meaning of such formalizations, as opposed to the meaningfulness
of the quantifiers they contain, extensionally, in terms of a pre-
established extant domain of actually existent entities.
As an alternative to Quine’s extensional criterion of ontological
commitment, we recommend an intensional criterion based on the
combinatorial analysis of being as maximal consistency. We can offer,
instead of Quine’s syntactical criterion of ontological commitment, a
more substantive criterion based on the combinatorial analysis of
being as maximal consistency. We can apply then the definition
directly in deciding what things or kinds of things exist, depending on
whether they satisfy or fail to satisfy the combinatorial analysis, with-
out invoking Ockham’s razor to include or exclude putative entities
according to the vicissitudes of variably and culturally unstable
perceived theoretical needs.
We say that to be is after all to be the value of a quantifier-bound
variable, but only provided that the variables in question range over
all logically possible objects in an ontically neutral semantics. Onto-
logical commitment is then achieved by the intensions of property
combinations, rather than whatever predetermined existent objects
belong to the extension of a corresponding predicate. Quine refers to
the objects that would need to exist in order for the propositions of a
theory to be true. What objects are these, we must ask, if they are not
intensionally characterizable logically possible objects? Are they such
objects as Quine elsewhere in his essay disparages as the possible fat
man in the doorway and the possible bald fat man in the doorway?
180 ONTOLOGY
Again, Quine maintains, speaking of the more ontologically generous
of his composite philosophical foils, benighted advocate of unactual-
ized particulars, the wily Wyman:
Wyman’s overpopulated universe is in many ways unlovely. It
offends against the aesthetic sense of us who have a taste for desert
landscapes, but this is not the worst of it. Wyman’s slum of
possibles is a breeding ground for disorderly elements. Take, for
instance, the possible fat man in that doorway; and, again, the
possible bald man in that doorway. Are they the same possible man,
or two possible men? How do we decide? How many possible men
are there in that doorway? Are there more possible thin ones than
fat ones? How many of them are alike? Or would their being alike
make them one? Are no two possible things alike? Is this the same
as saying that it is impossible for two things to be alike? Or, finally,
is the concept of identity simply inapplicable to unactualized
possibles? But what sense can be found in talking of entities which
cannot meaningfully be said to be identical with themselves and
distinct from one another? These elements are well-nigh incorrigi-
ble. By a Fregean therapy of individual concepts, some effort might
be made at rehabilitation; but I feel we’d do better simply to clear
Wyman’s slum and be done with it.
26
A theory on a combinatorial criterion of ontological commitment,
by contrast, is ontologically committed to the existence of the logical
objects that would exist if the theory were true. Unlike Quine, we are
not limited to quantifying only over existent entities in the extensions
of predicates, but freely refer to logically possible objects, regardless
of their ontic status. Quine is concerned about the identity conditions
for the possible fat men in the doorway. On the present theory, these
are distinct nonentities by virtue of having distinct submaximal
property combinations. The possible fat man is not the same as the
possible bald fat man, because their properties are different. Curi-
ously, Quine seems to have no trouble maintaining his grip on the
identity conditions for his distinct but presumably nonexistent albeit
logically possible fictional entities Wyman and McX.
Quine’s objection appears to misunderstand the concept of
unactualized possibilities, treating them as though they had actual
physical properties. If this were correct, then it would obviously be
absurd for several fat men, hirsute or otherwise, to crowd together
bumping shoulders, hips and elbows in the same narrow doorway. The
picture of unactualized possibilities that Quine’s criticism suggests, if
ONTOL OGI CAL COMMI TMENT ( ON QUI NE) 181
taken literally, is deeply problematic; but there is no reason to think of
nonexistent possible entities, intensionally constituted in their identity
conditions by submaximal property combinations, in anything like this
way. More importantly, the combinatorial criterion of ontological com-
mitment, essentially Wyman’s position, avoids the difficulty attributed
to Quine’s bound-variable criterion, whereby the ontological relativity
of a theorist’s ontological commitments entering into the investigation
of another theory’s ontological commitments inevitably results in the
kind of distortions of existence domain characterizations through the
limitations of the indeterminacy of radical translation. Limiting con-
cern to the ontically neutral logically possible objects of pure logic, we
do not need to survey another theory’s ontology through the coloured
lenses of our own attachments to a preferred existence domain, even if
our theoretical domain should happen to be extant.
If, on the other hand, we turn from quantifier-bound variables in
pure logic to the commitment-ridden bound variables of applied logic
as it is used, not externally by us from a metatheoretical perspective in
discussing another theory’s ontological commitments, but internally
by proponents of the theory in a way that is not intended to be
ontically neutral but committal, then we can say more substantively
that a theory is ontologically committed to whatever entities are
required by the theory to be maximally consistent, or that would need
to be maximally consistent, regardless of how they are designated, in
order for the propositions of the theory to be true. Appealing to a
syntactical bound-variable criterion of ontological commitment that
is at the same time wed to an extensional interpretation of proposi-
tional truth for predications, and that presupposes the actual exist-
ence of the entities in a preferred existence domain in philosophical
semantics, as Quine does, is certain to run into avoidable difficulties
of ontological relativity and indeterminacy of radical translation.
These implications are paraded as important discoveries in Quine’s
philosophy, but they should more properly be regarded as theoretical
embarrassments – signs of trouble in his syntactical criterion and
extensional interpretation of ontological commitment. Epistemic
inconveniences of such magnitude are symptoms of things having
gone drastically wrong in ontology, particularly when they are
permitted, as in Quine, to affect the shape of ontological commitment
assessments and do not merely subtend the quest for a preferred exist-
ence domain. They are a further indication of Quine’s mixing-up
applied scientific ontology with pure philosophical ontology that
follows inevitably from Quine’s semantic extensionalism, and is
preventable only by adopting an intensional combinatorial criterion.
Appearance, reality, substance,
7 transcendence
Scientific ontology
We now consider the first of a series of ontological commitments in
four traditional subscategories of applied scientific ontology. Shall we
follow the lead of other ontologists by distinguishing between appear-
ance and reality in a strong metaphysical sense? What shall we say
about the ontology of substance? Is there an argument to be made for
the transcendence of a certain part of the preferred existence domain
that is, in some sense, above and beyond, or in any case outside, the
actual world? What light does the combinatorial analysis of being as
maximal consistency shed on any of these time-honoured distinctions
in metaphysics and applied scientific ontology?
Applied scientific ontology is not the pure philosophical ontology of
being qua being but, so to speak, an annotated inventory of entities, in
which we offer good reasons for saying yes or no to including contested
entities in a preferred existence domain. It is here that we try to iden-
tify the ultimate kinds or categories of existent entities that we need, not
only for science but for all meaningful thought. In contrast with physi-
cal objects and physical states of affairs, we may find it necessary to
require convincing philosophical arguments to satisfy natural scepticism
about the existence of putative entities that we do not directly experi-
ence in sensation, such as abstract entities, especially numbers and
universals, propositions, minds and God. The same might also be true
for the concepts of imperceptible substance and transcendent entities.
Appearance, reality and substance sometimes go together in meta-
physics. In other theories, a sharp appearance–reality division is main-
tained independently of the concept of substance. Yet other doctrines
develop a complex concept of substance without taking special notice
of the appearance–reality distinction beyond its mundane occurrence
in optical and other kinds of perceptual illusions, artificial versus real
APPEARANCE, REAL I TY, SUBSTANCE, TRANSCENDENCE 183
flowers, and like phenomena, whose appearance and reality, so
construed, can be distinguished experientially through more patient
or acute observation of whatever is presented to sensation. Different
philosophies have used these terms in different ways, attaching
distinct and often incompatible meanings to the vocabulary. Although
we shall not try to sort out all of these ambiguities through the history
of philosophy in quite the detail or with the thoroughness they
deserve, we remain mindful of the alternative concepts that have
sometimes been advanced in applied ontology under the banners of
these common but often slippery concepts. The point holds with
respect to all four of these categories, with appearance arguably being
the least variable, and substance, transcendence and finally reality
itself occupying the most hotly contested philosophical territory.
Reality and the ontological status of appearance
We first explicate and briefly defend a particular interpretation of
these concepts, and consider arguments about the implications of the
combinatorial analysis of being as maximal consistency for inclusion
in or exclusion from a preferred existence domain of these four
putative applied ontological subcategories.
To speak of a distinction between appearance and reality in meta-
physics as opposed to epistemology is already to discredit appearances
ontologically. This is true in the philosophy of Plato, Descartes, Kant,
Schopenhauer, J. M. E. McTaggart and many other ontologists. Plato,
interestingly, does not try to argue for the distinction, but leans heav-
ily on Parmenides’ separation between the way of seeming and the way
of truth, the many appearances and the One reality in Parmenides’
monistic ontology, and the otherwise unsupported intuition that the
realm of being and truth must coincide for a domain of eternal
unchanging entities, appearances in the world as we experience them
notwithstanding, so that knowledge can only be of what is eternal and
unchanging in order to be itself also eternal and unchanging.
Why anyone should accept without further justification such a
concept of knowledge is unexplored in Plato and the surviving
fragments of Parmenides.
1
We either share their insight in this funda-
mental matter or we do not; we either agree and require no persuad-
ing that knowledge must be eternal and unchanging or we do not. For
present purposes, subject to reconsideration, in lieu of powerful
reasons to the contrary, we shall not throw in our lot with Plato and
Parmenides, but remain open-minded about other considerations that
might uphold a sharp metaphysical distinction between appearance
184 ONTOLOGY
and reality. As we shall see, reasons of this type have from time to time
been advanced in connection with the sometimes related concepts of
substance and transcendence. We as yet do not take account of any
compelling motivation to relegate true relevantly justified beliefs about
the world of experience as Plato does to the secondary status of right
opinion or mere belief in a likely story concerning the changing face of
phenomena, but stand behind the possibility of obtaining genuine
knowledge about the empirical world encountered in sensation.
Descartes, who in his famous motto claims to enter philosophical
disputes masked, Larvatus prodeo, raises the appearance–reality
distinction disguised as a deep metaphysical division.
2
Descartes’s real
interest is in the epistemology of clear and distinct perceptions as a
way of overcoming uncertainty about the actual state of the external
world, and in establishing rules for the guidance of empirical enquiry
in natural science based on purely rational foundations. The foun-
dations of knowledge for Descartes are supposed to be unshakeable
even when they concern the changing phenomenal world, and even
under the greatest imaginable threat to the veridicality of clear and
distinct ideas. Descartes envisions this threat to knowledge as taking
the form of a malignant demon, a fictional evil spirit that, for all we
know, conspires to deceive us when we exercise our senses in trying to
gather knowledge about the external world.
Descartes sees our only hope of epistemic salvation in a rational
demonstration of the existence and perfect benevolence of an
omnipotent all-knowing God, as the unfailingly veracious architect of
human cognition. Descartes thus holds up the spectre of a metaphysi-
cal division between appearance and reality merely as a dramatic ploy,
which he overcomes by philosophical–theological devices of a rather
unusual sort, in order to restore the distinction to its proper epistemic
application. In this way, he hopes to secure metaphysical gains in other
sectors of his philosophy, concerning the existence of God, the nature
of matter and the distinction between the body and soul. He argues
that if God vouchsafes clear and distinct perception, and if sensation
and inductive inference are appropriately chastened as to their limita-
tions within a special set of principles for avoiding error, then all of
science can enjoy the same high degree of epistemic certainty as
mathematics. The appearance–reality distinction, epistemically promi-
nent as it is in Descartes’s methodology, never assumes a permanent
place in his applied scientific ontology. It serves instead only
provisionally as a caution to unwarranted inferences, helping us to
avoid the equivalent of perceptual illusions throughout our scientific
reasoning. By recognizing the distinction between appearance and
APPEARANCE, REAL I TY, SUBSTANCE, TRANSCENDENCE 185
reality, we can prevent unwarrantedly jumping from the infallible data
of immediate sense experience considered only as such to inadequately
justified conclusions about the nature and actual state of the external
world through hasty insufficiently self-critical attention to the eviden-
tiary requirements of science.
3
Kant is another historical figure who, like Plato but in different ways,
is committed to a metaphysical distinction between appearance and
reality in his applied ontology. Kant does not separate the world of
appearance from the world of reality in the manner of Plato and
Parmenides, but identifies two incongruent aspects of a single unified
world: the phenomenal and the noumenal or thing-in-itself (Ding an
sich). Schopenhauer follows Kant more closely in this crucial respect
than in other areas of Kant’s philosophy. Although Schopenhauer
forgoes reference to noumena in deference to the Kantian thing-in-it-
self, he also distinguishes between the world as Will (Wille) and as idea
or representation (Vorstellung). Kant’s and Schopenhauer’s division
between appearance and reality thus has real applied ontological bite.
While Schopenhauer credits Kant’s distinction as among the greatest
contributions to the history of philosophy, he faults Kant for not
remaining true to the dichotomy between phenomena and noumena.
4
Schopenhauer denies that the principium individuationis for identify-
ing, individuating or discriminating among distinct things can possibly
apply to thing-in-itself, which he argues is altogether beyond the reach
of any explanation of its number, condition, origin or the like, under
the four-fold root of the principle of sufficient reason, consisting, as he
characterizes it, of laws for understanding the logical, mathematical,
causal and moral properties exclusively of phenomena in die Welt als
Vorstellung (appearance, presentation or idea).
5
All this leaves us with more unsaid than said, and more that should
be said in order to appreciate the history of these philosophers in the
ontology and epistemology of appearance and reality. To proceed, let
us turn to the relevant applied ontological issues, taking our brief
introduction to philosophical treatments of the appearance–reality
distinction as background to an ontological investigation of appear-
ance, reality, substance and transcendence. We shall concentrate on
what can justifiably be concluded about the meaning and usefulness of
each of these applied ontological subcategories.
Appearance and reality in combinatorial ontology
What should we think about the alleged distinction between appear-
ance and reality? Are there good reasons based on the combinatorial
186 ONTOLOGY
analysis of being as maximal consistency to distinguish between the
way the world appears to sensation and the way it is in reality? Should
we try to restore a sense of the metaphysical distinction that is more in
the spirit of Plato, Kant and Schopenhauer? Or should we think of the
appearance–reality distinction as more superficially epistemic, merely
a matter of avoiding illusion and certifying veridical perceptions, in
the manner of Descartes?
One consideration is that without the distinction it may be impossi-
ble to avoid the consequences of ontic idealism. As with Plato’s
commitment to the idea that knowledge can only be of what is eternal
and unchanging, we need to recall what it is that is supposed to be so
bad about idealism. Critics of idealism sometimes assume that there is
a slippery slope from any type of idealism to wilful subjectivity, as
though to be an idealist of any stripe is automatically to accept the
fantastic thesis that individual thinking subjects can will the world or
the exact state of the world into existence. Idealism, even of more
objective ambitions, is often said to offend against a robust sense of
reality, without which ontology is cut adrift from science. There are
idealisms, like Berkeley’s, that have defied this objection. Let us
nevertheless assume that the criticism is correct, and that idealism is
objectionable, if for no other reason than because of its inherent
subjectivity. It is argued that idealism is the unwelcome result if we do
not distinguish between appearance and reality by allowing appearance
to occur within the mind, as a sequence of sense impressions and stream
of ideas or psychological contents, reserving for reality the existence
and state of substances outside the mind in external reality, or, alterna-
tively, in the Kantian thing-in-itself or Schopenhaurian world as Will.
The crux of the argument is that if we limit applied ontology to the
way the world appears to thought, especially in immediate sensation
and memory, if there is no reality beyond appearance in the content of
thought, then the world is nothing but a series of ideas in the mind.
This is a conclusion that philosophers, like Berkeley, who have
warmly embraced idealism want not to avoid but to enthusiastically
accept. To prevent reality from collapsing into appearance in the sense
of purely mental occurrences is to require applied ontology to posit a
mind-independent reality or substance, the real matter of the external
world. The substance of the world as opposed to our sensation and
thought about it can then be said to possess primary qualities like size,
weight and the other properties of physical substances, as studied by
physics. The objective properties of substance are further opposed to
secondary qualities like colour, taste, smell and the like, as studied by
psychology, that seem to belong to thought, to the mind of the
APPEARANCE, REAL I TY, SUBSTANCE, TRANSCENDENCE 187
perceiver. If applied ontology does not posit such a realm of
substance, then we seem driven to some version of idealism, which is
often assumed to be a worse fate.
6
The dilemma is that if, in order to escape idealism, we try to estab-
lish a metaphysical appearance–reality distinction in this way, then we
seem forced to accept an equally if not more unwanted conclusion,
that there exists something that is essentially unknowable, but is
supposed to possess definite properties and stand in relations to other
things. This something, an unperceivable philosophical or metaphysi-
cal substance, if we are consistent, must then be acknowledged as
transcending all experience. It will be, as John Locke, who was
attracted to this kind of solution, and who adduced a version of
Galileo’s distinction between primary and secondary qualities in its
defence, notoriously described in An Essay Concerning Human
Understanding, in the French adage, a Je ne sais quoi: a something I
know not what.
7
Otherwise, we might be tempted, like Kant, despite
the threat of idealism, to adopt a concept of the noumenal thing-in-
itself, or Schopenhauerian aspect of the world as Will, existing
independently of thought and the mind’s pure forms of intuition or
sensation, beyond all concepts and categories of the understanding.
By embracing the appearance–reality distinction in this form, we
are driven from idealism to a kind of mysticism. We are then obliged
to accept the existence of something for which we have no evidence
and which we cannot come to know in any meaningful way. Schopen-
hauer in this vein appears in his own way to go too far by declaring the
thing-in-itself to be Will, thus imposing a kind of character on what is
supposed, even by Schopenhauer, to be descriptively unknowable, by
virtue of falling outside the scope of the four-fold root of the principle
of sufficient reason. To attribute a nature of any kind on the world in
reality or thing-in-itself even metaphorically, for Schopenhauer,
should be the height of treason to his own philosophical principles.
For in the Vedic myth that Schopenhauer adapts to his purpose it is
only to drape another fold of the veil of Maya over the empirical
inscrutability of reality.
8
We are just as hard-pressed by the demands of a robust sense of
reality in the train of modern science to maintain that something exists
for which we have no experiential evidence as we would be to accept
the idealist conclusion that everything exists within the mind. This
would be a regrettable consequence even or especially in the case of a
supposedly objective idealism, as in Berkeley’s ontology, where sensi-
ble things exist archetypally in the infinite all-knowing mind of God,
and ectypally in their parts, aspects and fleeting moments in the finite
188 ONTOLOGY
minds of human perceivers.
9
From the standpoint of the combinatorial
analysis of being as maximal consistency, it might be said that the
idealist side of the dispute at least has the advantage of not giving up
epistemic access to the existence and constitutive properties of real
entities. The combinatorial analysis construes these as a combination of
ideas of an object’s properties, whereas substance theory, in the sense
being considered in contrast, posits the existence of an entity that has
no knowable properties. Substance in that sense amounts to under-
standing all existence as a logical object of pure logic, a bare particular
or individual predication subject lacking any properties whatsoever,
about which we cannot possibly know anything. Far from satisfying the
requirements of maximal consistency, such a concept deprives reality of
properties. The category of substance should presumably be rejected
from applied scientific ontology as failing to satisfy the combinatorial
requirements of predicational maximal consistency for an existent
entity. The only exception could be if we are willing to accept a sense
of predicational maximal consistency that is inherently concealed from
epistemic access behind the phenomena–noumena distinction or
Schopenhauer’s veil of Maya. If such a conclusion is intolerable in the
metaphysics of science, then we should find the implication logically
incompatible with the combinatorial analysis of being as maximal
consistency.
Does this mean that we should instead swing over to some version
of idealism in order to remain true to the maximal consistency
analysis of being? To avoid both idealism and mysticism in applied
scientific ontology it must suffice to deny the existence of substance in
the Lockean sense that Berkeley rejects or as Kantian or Schopen-
hauerian thing-in-itself on the grounds of denying all logically possi-
ble epistemic access to an entity’s maximally consistent property or
states-of-affairs combination. The assumption that we cannot im-
mediately say which of these choices is right already indicates difficul-
ties in the concept of Lockean substance or Kantian thing-in-itself.
The Lockean concept of substance or Kantian thing-in-itself does not
fit the combinatorial concept of being neatly, if at all, for we do not
know what to say about it. If substance or thing-in-itself is a world,
then we are back to Plato’s two worlds conception, and we must deny
the reality of the perceived world in order to preserve the unique
actuality of an intelligible world of abstract entities. If substance or
thing-in-itself is only a part or aspect of the actual world, then its
ontological or epistemic predicational incompleteness threatens the
completeness of the actual world, and as such is excluded by the
combinatorial analysis of being.
APPEARANCE, REAL I TY, SUBSTANCE, TRANSCENDENCE 189
Idealism is avoided by denying the questionable assumption that
entities are constituted by particular appearances rather than by the
actual properties themselves. Such properties, in the case of physical
entities, are always logically possibly or, in principle, epistemically
accessible to perception, but do not need to be identified with corre-
sponding appearances. The identification of constitutive properties
with perceptions or ideas is the core of Berkeley’s radical empiricism,
phenomenalism and idealism. Why, in the first place, should anyone
have ever supposed that they were identical? It is too important and
controversial a thesis to be taken for granted, but it is difficult and may
finally be impossible to argue with anyone who does not already share
the intuition. We have now considered several reasons not to accept its
truth, regardless of how reasonable it is made to seem. If we disapprove
the thesis, then we avoid idealism and are free to accept some form of
nobly naive realism sufficiently robust for the metaphysical underpin-
nings of empirical science. The appearance–reality bifurcation in that
case endures as in Descartes only as an epistemological distinction
between the way things under certain conditions can sometimes
misleadingly appear, and the way we judge them on more careful
inspection or sober reflection to be in reality. Thus, we learn to see
through the fata morgana, to judge true and false friends, as phenom-
ena here before us in the publicly accessible empirical world.
It is not only the appearance–reality duality that is displaced in this
way as an epistemic rather than metaphysical concept, but, more
importantly, the concept of an unperceivable substance. Instead of
thinking of substance as existing outside thought, a more plausible idea,
that is in some ways more traditional, going back to Aristotle’s defini-
tion of ousia as informed matter, or of substance as we ordinarily think
of it in the sense of material or physical stuff, can be advanced in an
empirical scientific framework. Substance in this more familiar less
philosophical sense is equally influential in the history of philosophy,
but belongs more properly to the topic of physical entities or material
constituents of the actual world. The advantage of the empirical
Aristotelian concept of substance as perceivable informed matter is its
immediate compatibility with the combinatorial analysis of being.
Transcendence of the physical world
We are left only, in this category, after our evaluation of appearance,
reality and substance, with the concept of transcendence. What is
meant by transcendence? Should we consider transcendent entities to
be included in or excluded from a preferred existence domain? Does
190 ONTOLOGY
the combinatorial analysis of being as maximal consistency encour-
age, discourage, permit or exclude transcendence?
Intuitively, the idea of transcendence is the idea of something that
is beyond the world of appearance or experience. Lockean substance
with its primary qualities measurable by science does not transcend
the world, but the Kantian thing-in-itself or Schopenhauerian Will is
a transcendent aspect of the phenomenal world. Thing-in-itself stands
outside the world as it appears to thought, and, as the term suggests,
transcends the cognitively available world. The Kantian or Schopen-
hauerian thing-in-itself is only an example of the only kind of thing
some philosophers have claimed to transcend the world of experi-
ence. Thinkers as diverse in their methodologies and ontological
commitments as Kant, Schopenhauer, Husserl and Wittgenstein have
held that the self or metaphysical subject of thought and experience
transcends the actual world. In the Tractatus, Wittgenstein further
maintains that logical form, pictorial form, form of representation,
the sense of the mystical or grasp of the world as a whole sub specie
aeterni, and especially ethics and aesthetics, which in his early
philosophy he considers as one along with other kinds of value,
transcend any logically conceivable world construed as a structure of
states of affairs in logical space. In many religious traditions and
philosophies of religion, God is also often claimed to be transcendent,
to transcend the world of experience or physical spatiotemporal
order that God may be believed to have created or over which God is
sometimes believed to rule and judge.
The concept of transcendence is appealing for a variety of reasons.
We shall begin, for simplicity’s sake, by considering transcendence in
the case of aesthetic or moral value. The conclusions we reach for
these examples should nevertheless be sufficiently general, having to
do with the concept of transcendence. If the implications are correct,
then they apply to any theory of transcendence, including thing-in-
itself, value, form, God or any other theoretical transcendentalia. The
combinatorial argument against transcendence is that the analysis of
being as maximal consistency precludes transcendence even as a
logical possibility. According to combinatorial pure philosophical
ontology, the actual world is maximally consistent, leaving no possi-
bility for truths or facts or states of affairs involving true predications
other than those already contained in the actual world’s states-of-
affairs combination. The conclusion may count against combinatorial
ontology for those who are firmly committed to the transcendence of
value or other entities or factors, but we should not be dissuaded by
such considerations unless they are backed by sound arguments.
APPEARANCE, REAL I TY, SUBSTANCE, TRANSCENDENCE 191
The intuitive case for the transcendence of value is, in large
measure, the desire to strike a philosophical compromise between
eliminating value altogether from the preferred existence domain as
simply nothing, and recognizing that value is not an ordinary perceiv-
able physical or spatiotemporal property of physical things. We do
not ordinarily believe that we perceive the beauty of a painting or the
evil of a murder when we see the pigment on canvas or a murderous
act being perpetrated. Value seems to be something that is superadded
to these physical entities and real-world states of affairs. Where is
value? Except in the most philosophically inexact colloquial sense,
the question does not really have an answer, which may be equivalent
to saying that the question is unintelligible. If value literally has no
place in the actual world, then it might reasonably be said, in so far as
value has being, to be transcendent, and as such to transcend actual
existence or to exist in a transcendent ontological order, like the non-
spatiotemporal realm of abstract Platonic entities. It is in something
like this sense that Kant’s thing-in-itself or Schopenhauer’s world as
Will is supposed to transcend the phenomenal world of appearance.
Although not itself part of the world, a transcendent entity is meta-
phorically, but not of course literally, above and beyond the actual
world – in some sense outside the physical spatiotemporal framework
of the actual world. Do we have a clear concept of such a thing?
The actual world contains all and only existent entities and states
of affairs. If to exist is to be maximally consistent, then the maximal-
ity, the predicational completeness of the uniquely actual world,
precludes anything existent, anything actual or partaking of being to
exist above, beyond or outside the actual world. There could only be
transcendence, presumably, but also paradoxically, if the transcendent
entities in question were nonexistent nonentities, or if transcendent
entities, despite themselves, were nevertheless a part of the actual
world. We are confounded if we try to pursue this line of thought, the
only relief from which seems to be to deny that there are transcendent
entities possessing any mode of being if they are not physically
integrated into the actual world. If, on the other hand, we try to
include transcendent objects in the preferred existence domain, then
they can no longer be described as transcending the actual world,
which consists of all and only actually existent facts and objects. From
the standpoint of the combinatorial analysis of being, the idea of the
transcendence of the actual world by transcendent entities is logically
incoherent. Transcendent entities cannot exist, for either they are not
transcendent, or they are not entities of the actual world interpreted
as a maximally consistent states-of-affairs combination. As with the
192 ONTOLOGY
non-actuality of merely logically possible worlds that are predica-
tionally consistent but incomplete, the predicational maximality of
the actual world logically uses up all of the logically possible predica-
tional completeness, leaving only submaximally consistent property
and states-of-affairs combinations left over for non-actual merely
logically possible entities that by definition are incomplete, allowing
no logical space to be occupied by non-physical non-spatiotemporal
transcendent entities.
What, then, of the ontology of value? There are several kinds of
explanation that avoid commitment to the existence of transcendent
entities. We can understand the value of a painting or murder as a
psychological projection of attitude by persons reacting in some sort
of causal relation with a valued object. Or we can think of value as an
abstract and hence imperceptible entity or property of perceivable
things, if there should turn out to be abstract entities. We might,
finally, think of value as an individual rather than universal but
supervenient property that in some sense arises or emerges from or
supervenes on an object’s ordinary properties, as a consequence of
their coinstantiation.
10
If we have a variety of options for interpreting
aesthetic and moral value non-transcendentally, then we can admit
that we are not forced by the facts for which an adequate theory of
value must account into concluding that there must be transcendent
entities. At least we need not be ontologically committed to the exist-
ence of transcendent entities on the grounds that there are values or
valuable things, and that values are not experienced as ordinary
spatiotemporal physical properties. We are not yet compelled by any
argument we have considered to accept transcendent existence, or a
realm of transcendent entities, of transcendence as a positive applied
scientific ontological category of genuine being. We have as yet no
good reason to extend applied scientific ontology to include tran-
scendent entities, and we have stronger philosophical justification in
combinatorial ontology for rejecting the category of transcendence
and the concept of a transcendent entity as logically incoherent.
Physical entities: space, time,
matter and causation, physical
states of affairs and events,
8 natural laws
A material–physical world
The category of physical entities is usually supposed to be the least
metaphysically problematic in applied ontology. The question for a
preferred existence domain is not whether physical entities exist.
Their existence can be assumed as established by combinatorial pure
philosophical ontology, on the assumption that there are non-actual
logical possibilities, and hence distinct logically possible worlds, that
all states of affairs logically must either be spatiotemporal or non-
spatiotemporal, and that only physical or spatiotemporal entities can
distinguish one logically possible world from another.
The existence of physical entities is further confirmed by empirical
experience of the actual world in sense perception. To begin with,
scientific knowledge of the actual world, impermissible in pure philo-
sophical ontology, is unobjectionable and in many ways indispensable
in applied scientific ontology. As we turn to pure logic to get started in
pure philosophical ontology, so we turn to empirical science to get
started in understanding the nature of physical entities in applied
scientific ontology. As a result of our experience of the world we
know that there are real existent external physical entities and states
of affairs, and we can make progress towards the development of an
appropriate applied scientific ontology of physical entities by looking
to what are judged to be the most successful natural sciences as a start-
ing place for articulating an applied ontology of physical entities from
the standpoint of the things and kinds of things such theories need to
posit in their respective preferred existence domains in order to
sustain the truth of their principles, assumptions and conclusions.
194 ONTOLOGY
Combinatorial ontology of space and time
The main task of an applied ontology of physical entities is to identify
a structure of ontic subcategories for all philosophically interesting
types of physical things. Space and time can be classified as physical
entities, even though they are not generally thought to be perceivable
as such, when physical entities are perceived in space and time or
spacetime.
Space and time are physical preconditions for the existence of
perceivable physical substances. Kant’s transcendental aesthetic holds
that space and time are pure forms of intuition, which is to say sensation
or perception. As pure forms of intuition, space and time must be
brought by a subject to experience, because they are impossible to
derive from or discover within experience by a subject who is not so
pre-equipped a priori. Without space and time as pure forms of intui-
tion, Kant argues, physical entities could not be experienced as a
distribution of cognitively distinct and discrete spatiotemporal objects
in what Kant calls the sensible manifold. The world that would appear
to us in that case when we opened our eyes would not be objectified, but
would be nothing but a sheer chaos without definite shape or patterns
of colour, and with no possibility of mentally keeping track of whatever
passes through consciousness from moment to moment in time.
What would that be like? It is surely unthinkable, unintelligible for
us even to imagine anything we would be prepared to recognize as
experience, just as Kant says, without definite shape or colour, and
unaccompanied by any sense of the passing of time in which we
ordinarily live through the flow of thoughts and images. The
experienceability of things in space and time, and in particular places
in space, is a function of the perception of extended sensibles and of
sensibles as extended. The temporal properties of things similarly
presuppose time as a pure form of intuition by which things are
experienceable as enduring and remaining the same while undergoing
accidental changes, as Aristotle says. If we were not already pre-
equipped with space and time as pure forms of intuition, our minds
would never be capable of discovering them in the flux of experience
for which no sense of change, no shape or coloured places or the like,
could possibly be discerned.
1
Space and time in Kant’s technical terminology are part of the
transcendental ground or ultimate metaphysical presuppositions of
intuition. Space and time are nevertheless entities that have many
properties, and are involved in innumerable relations. Kant’s absolut-
ist Newtonian conception of space and time entails overlapping
infinitely extensive and infinitely divisible rectilinear spatial grids
PHYSI CAL ENTI TI ES 195
suffused with an infinite unidirectional flow of time that marks the
changes of state of physical entities within a causal matrix in the mind’s
experience of objectified external reality. All these facts depend on the
physical properties of space and time or spacetime as physical entities.
Moments of time, like regions of space, are logical objects with physi-
cal properties. As such, they are entities like any others, if, as it seems
unobjectionable to assume, they are predicationally consistent and com-
plete, and relationally interwoven with the physical properties of physi-
cal entities like particles of matter, macrophysical complex objects and
fields of force that make up the physical universe. If it seems odd to
count space and time as physical entities more or less on a par with
physical entities in time and space or relativistic spacetime, it is likely
to be because space and time or spacetime are intuitively understood as
something more like a medium in which physical entities exist, rather
than physical entities themselves.
Such a distinction will not stand scrutiny. There is no sound basis for
distinguishing a medium of other physical entities as itself something
other than a physical entity. Space and time or spacetime evidently have
properties like other entities, although they are not like spatiotemporal
entities in other ways, and there is no immediate cause to suppose that
they are logically inconsistent or predicationally incomplete, arguments
of sceptical metaphysicians like Parmenides, Zeno of Elea and
McTaggart notwithstanding.
2
Space and time or spacetime are perhaps
an unusual kind of physical entity, but an entity that is presupposed by
the existence of objectified micro- and macrophysical entities nonethe-
less. Without space and time, the ordinary objects of experience that we
think of more paradigmatically as physical entities would be relationally
incomplete, with predicational gaps, contrary to our usual understand-
ing of the external physical spatiotemporal world.
Even if spacetime is the special medium in which the causal matrix
of physically interrelated spatiotemporal physical entities have their
being, as in Galileo, Descartes, Newton, Leibniz, Locke and Kant,
that is no reason to discount the existence of space and time or (here-
after) spacetime as real physical entities. Many types of physical
media also exist in the same sense as, even if in a different way than,
the physical entities in which they exist. As examples, we may think of
the sea and its creatures, a culture broth and its multiplying micro-
organisms, a radio wave and the information it transmits, a line of ink
and the thoughts it expresses. We have grown accustomed to the idea
that many different kinds of physical entities exist, not all of which by
virtue of being physical are necessarily physical entities belonging to a
single unified subcategory.
196 ONTOLOGY
If spacetime is maximally consistent in its property combination,
then it satisfies the combinatorial analysis of the concept of being;
according to the combinatorial analysis, therefore, spacetime exists. It
is a physical entity, moreover, in the required sense, rather than
abstract. It would be untenable to consider spacetime to be non-
spatiotemporal, which is sufficient to classify spacetime as physical
rather than non-physical or abstract. To include spacetime as an exist-
ent physical entity is not to begin to consider its physical and
metaphysical complexities. That is a topic that remains for science
and philosophy to explore beyond the mere ontological commitment
to spacetime’s existence as a physical entity.
Matter as the substance of physical entities
We have already considered substance in the eighteenth-century sense,
where, idiosyncratically from a contemporary perspective, it is synony-
mous in the writings of philosophers like Locke and Berkeley with
insensible mind-independent matter. We have also suggested that this
is a problematic and to that degree uninteresting concept in contrast
with the idea of substance or matter as experienceable physical stuff.
Matter, in the physical spatiotemporal sense, is clearly existent
according to the combinatorial analysis of being. To confirm that this
is true we need only identify good reasons to believe that physical
substances in the material universe are predicationally maximally
consistent. Physical objects in this sense are paradigmatically maximally
consistent, whether we think of matter generally as the ultimate physi-
cal stuff, the chemical molecular and atomic constituents of all other
relatively more complex physical entities, or specifically as the particu-
lar physical entities themselves, regardless of their respective levels of
complexity or constitution out of simpler substances.
Our senses, even hearing and taste, are three-dimensional in the sense
that they provide spatial information about physical entities. We never,
and certainly never simultaneously, experience all the aspects of a physi-
cal entity. At most we see one side of an apple, one part, and from one
perspective of its external surface. No matter how finely we slice and dice
a material entity, we can only experience even the most transparent
object from the outside. We thereby confront a fundamental opposition
between subjectivity and the objective world. We know that there exists
more than we immediately or through the course of human history will
ever experience of even the most closely studied physical entity.
The dynamic object, C. S. Peirce has said, is phenomenally
inexhaustible. Nicholas Rescher has recently reaffirmed this first vital
PHYSI CAL ENTI TI ES 197
truth of any understanding of the concept of a physical entity in the
context of explaining the multiplicity of perspectives that differently
situated objective observers of the same physical phenomena can
experience. A similar concept enlivens Husserl’s theory of the
endlessly receding phenomenological horizons presented to thought
in the transcendental epoché. We find much the same idea again if we
go back to Johann Wolfgang von Goethe and Jean-Jacques Rousseau,
who marvelled poetically at the inexhaustible riches of a single blade
of grass.
3
We know, as a result, that there is more to the existence of
the physical world than will ever meet the eye, as a blade of grass rep-
resenting any and all physical entities serves to remind ontology.
Physical states of affairs as events
We do not question the actuality of physical states of affairs. We have
in fact already acknowledged the combinatorial necessity that
transworld-variant physical states of affairs exist in order to prevent
all logically possible worlds from collapsing into the actual world. It is
only physical states of affairs, different in distinct logically possible
worlds, that can possibly distinguish one logically possible world
from another. Abstract entities, putatively speaking, including
abstract states of affairs, either do not exist at all or exist alike in every
logically possible world.
This is the right way for things to turn out. It is not a choice we
make in order to obtain a desired philosophical outcome, but one that
logically must occur within the totality of all logically possible states-
of-affairs or object–property combinations. It is a conclusion we
could not prevent even if we wanted to had we found it metaphysi-
cally unpalatable. As it is, the combinatorial implication gives us just
the expected result. We have, and combinatorially we must have,
logically contingent physical objects and physical states of affairs,
which is at once to say also that we have, and combinatorially must
have, logically contingent physical entities at all descriptive levels of
the ontic hierarchy. It is gratifying to see that this is precisely what we
demand from an adequate concept of the actual world, and that the
combinatorial analysis of the concept of being delivers the account
without heroics. We identify physical states of affairs with physical
events, if by a physical event we mean a physical state of affairs that
occurs in and at a particular region of spacetime. By speaking of a
physical event we only emphasize the spatiotemporality of a physical
state of affairs, where combinatorially there are no physical states of
affairs that are not physical events, and conversely.
198 ONTOLOGY
Causation and causal connections
Causation falls somewhere between spacetime and material substance.
It is not itself a physical entity, but more relational like spacetime, and
is itself a spatiotemporal phenomenon. Where spacetime seems to be
more entity-like in sustaining predications that have a strong presump-
tion of maximal consistency, causation, as Hume taught, is nominal –
merely the name we give to our idea of certain types of regular
sequences of physical events. We call an event a cause of another event
when, according to Hume, the two types of events exhibit constant
conjunction, temporal succession, in which causes always precede
effects in time, and spatial propinquity. The propinquity condition
requires that physical entities in causal connections physically touch or
otherwise come into direct contact, disallowing action at a distance.
Modern science hypothesizes causal connections occurring by way of
the respective fields of several types of attraction and force, themselves
evidently causal concepts, surrounding material entities.
If Hume’s enquiry is limited only to the origin of our idea of causa-
tion, can anything more definite be said about causation to indicate
that it might be a physical entity according to the combinatorial analy-
sis of the concept of being? If we think of physical states of affairs or
physical events as physical entities, and of causes and effects as physi-
cal events, then we cannot avoid classifying causes and effects as
physical entities. This is a relatively uninteresting, even trivial, sense
in which causation is construable as a physical entity. What about
causation itself? Is there also a physical entity, or any other type of
entity, that links together events when one is the cause of the other?
Some philosophers have thought of causation in something like this
way: as a real force or binding energy, the cement of the universe, in
Hume’s phrase, holding all things in relation and stringing them
together in the complex spatiotemporal world of the physical uni-
verse considered as a vast interconnected causal matrix.
4
Such specu-
lative meta-physicians cannot understand causation as something so
watered-down as to involve nothing more than Hume’s three-part
analysis appears to imply. They object to the idea of causation as no
more than a certain pattern of relations among existent events in the
actual world, a sequence of events that could be disconnected and
logically altogether different than it actually is, even totally random,
with no identifiable cause-and-effect relations as real physical entities.
Causation seems to many philosophers to be something more; we
can count on it so reliably. To flip a light switch or boil an egg, to make
or do any of the things we do, to pilot the space shuttle or perform
successful brain surgery, is to know that certain types of events that we
PHYSI CAL ENTI TI ES 199
can try deliberately to produce will undoubtedly be followed by
certain other types of events. We generally know what we are doing
when we take hold of things, until mishap indicates that we must
refine our understanding of causal connections and how and where
causation obtains. We never, on the contrary, find ourselves obligated
to soften our concept of the necessity with which an effect follows its
correlated cause. Technical specialists who exercise control over an
aspect of the physical world, to the limited extent that human
decision and skill make this possible, can judge with remarkable
accuracy precisely how the world will behave when we do this or that.
As for things that we have not encountered before, we have relatively
well-refined but open-ended flexible ways of proceeding to find out
about unknown physical substances and causal relations among physi-
cal events, that enable us to venture confidently also, armed with the
tried and tested procedures of scientific method, into the unknown.
These are commonplace facts not to be despised but to be appreci-
ated and understood. They presuppose a specific concept of causal
relation that we would do as well to explicate. Should this concept be
thought of as that of a physical entity? We have already argued that
spacetime is a special type of physical entity, an actual thing in the
actual world. Although this goes against several prominent philo-
sophical traditions, our purpose is not to fall in line with other meta-
physical systems, but to think these things through for ourselves.
Why, then, should we not say basically the same about causation, and
recommend reifying causation and causal connections in the great
network of physical events as itself an existent physical entity? Why
not regard causal connections as real physical entities in their own
right? If space and time and matter all have being, why not causation?
The answer is that causation already has being by virtue of relating
real physical entities and states of affairs in the actual world. There is
nothing further for the being of causation to consist in anyway, and no
other basis for the existence of causation that would need to be
invoked in order to construe causation as a separate entity. It is, after
all, not so weak or watery a fact for actually existent events to be so
related as to exhibit regular reliable patterns of constant conjunction,
temporal order and spatial propinquity. It is sufficient in any case to
account for the confidence with which technical experts in engineer-
ing and the applied sciences causally manipulate the world, reaching
out with their Zuhandenheit, if they so choose, as non-experts also do
in acts of everyday causally efficacious agency, using a hammer or a
telephone, or doing anything at all. We do not need to consider any-
thing more than Hume’s three conditions to establish the existence of
200 ONTOLOGY
causal connections in the actual world – a rather different situation
than that involved in positing spacetime as a physical entity.
Causation does not need to be anything else, other than the actual
events of the world falling out in such a way as to constitute regular
patterns of the sort identified by causal principles and formulated as
natural laws for purposes of inductive reasoning. We do not need to
suppose that anything more or over and above and in addition to
existent events in the actual world exists in order to explain the reality
of causal connections as existent physical entities. It is not a question of
affirming or denying the reality of causal connections. Causation in that
sense is as real as any actually existent entity or state of affairs. It is a
question only of understanding what it means for a causal connection
or causation considered as such to be real. If Hume is on the right track,
then it need be no more than to say that physical events causally related
one to another by Hume’s three conditions are actual. This is not to
deny or affirm the modal status of causal connections as logically nec-
essary or contingent. If the previous argument concerning the logical
contingency of constitutive physical states of affairs in the actual world
in pure philosophical ontology is correct, then every causal connection,
causation as such in the actual world, is equally logically contingent, and
ultimately a matter of the same logical random probability or pure
chance that we have previously described as combinatorial roulette.
Within a framework of combinatorial analysis in pure philosophi-
cal ontology, we say that the being of causation or of particular causal
connections is explained by the three conditions of Hume’s account
of the origin of the idea of causation. For causation to be a real physi-
cal entity over and above the real physical events that are causally
related to one another by the conditions of Hume’s theory on the
combinatorial analysis would be for it to be, as it presumably is, a
maximally consistent predication subject. We are correct, in that case,
to consider causation as something real, an existent entity possessing
being at the level of relations among physical states of affairs in the
actual world, as real as the entities it relates. We are not, on the other
hand, required to suppose that the being of causation or causal
connection consists in something over and above the real being of
causally related physical events, nor that there is real causation in
non-actual merely logically possible worlds.
Causal inefficacy of natural laws
We have said that natural laws codify causal connections between physi-
cal events at a higher level of abstraction. It is strange and unnecessary
PHYSI CAL ENTI TI ES 201
to reify natural laws, particularly if we have not made distinct applied
ontological provision for causation or causal connections. We can think
of natural laws as convenient formulations of causal regularities that by
chance prevail throughout the physical universe. Natural laws thus take
on whatever causal necessity obtains among the regularities themselves.
This modality, while not as strong, or, in another way, as weak, as logi-
cal necessity, is still strong enough to instil confidence or dread in the
law-like causal stability of the actual world, and in our continuing ability
to influence events in the physical universe.
To refer to a natural law is to invoke the authority of whatever
causal regularities occur throughout the actual world. Alternatively,
to mention a natural law is to speak of a principle or proposition,
often thought to be an abstract entity or a meaningful sentence or set
of sentences, that does not seem to be a likely candidate for causal
efficacy or actually making things happen in the physical realm of real
physical entities and events. If we are to take a stand for a preferred
existence domain in this part of applied scientific ontology, then we
might be inclined to argue that a natural law is best understood as a
useful description of the causal regularities that happen to hold
among existent physical events in the actual world, and that natural
laws are expressed by means of principles or propositions that by
themselves do not need to be thought of as in any way causally effica-
cious, except indirectly in so far as they influence thought and action.
It is among causally related real existent physical events that the
causal efficacy of natural laws is to be found, rather than in their
linguistic and mathematical formulation as natural laws.
The truth of a natural law that applies to real existent physical
events in the actual world is at most logically contingent, actual and
presumably causally, but not logically, necessary. If natural laws exist in
any other, third, sense, beyond representing actual relations among
existent entities and existent physical events, superseding the existence
conditions for natural laws construed only linguistically–mathemati-
cally as principles expressing these relations, then, according to the
combinatorial analysis of being, natural laws like any other physical
entities must be maximally consistent. Such an interpretation does not
seem to be either well motivated or intrinsically plausible. It costs us
nothing to say that there are natural laws in both senses of the word we
have now considered. This is true if only because there are causal regu-
larities, and because there may also be principles and propositions if
not as existent abstract entities, then at least as concrete particulars or
types thereof whose property combinations are maximally consistent.
As with causation and causal connections, we have no justification for
202 ONTOLOGY
going beyond these harmless admissions to the preferred existence
domain of an applied scientific ontology by maintaining that causation,
causal connections and natural laws are actually existent physical
entities over and above the regularities by which physical states of
affairs or physical events that happen to exist in the actual world are
related.
The same style of reasoning must apply to the consideration of any
other category of putative physical entity. We must in every case
evaluate the merits of a candidate entity according to the combinato-
rial analysis of being. We must try to determine whether or not the
putative entity in question can be considered first and foremost as a
purely logically possible object with a maximally consistent property
or states-of-affairs combination. If so, then we can justify the intro-
duction of a new entity or type of existent physical entity in a new
category to add to the preferred existence domain; if not, then we are
not entitled to include the discredited would-be entity. We have seen
no good reason to pursue either of these directions here, but conclude
our inventory of the types of physical entities in the existence domain
with the above-mentioned entities: material substances, space, time or
spacetime, physical states of affairs or events and, derivatively, causa-
tion in the sense of causal connections holding between actually
existent physical events.
Incompleteness in quantum phenomena
There is a peculiar problem that stems from the quantum indetermi-
nacy thesis in contemporary microparticle physics. As it may appear
to affect the predicational completeness of physical entities, it is a
topic that we should finally address. What are we to say about a
physical entity like a tiny quark, or, say, an electron composed of
quarks, if the judgement of modern physics is that these particles are
indeterminate in their constitutive spatiotemporal properties?
Quantum indeterminacy, realistically interpreted, entails that no
quantum-sized particle can have both determinate position and deter-
minate momentum. To discover one of these paired properties we
must physically interact with the particle in such a way as to disturb
the object, thereby changing the complementary property. Determine
a particle’s position and we alter its momentum; determine its
momentum and we alter its position. If position and momentum can
never be simultaneously determined for quantum phenomena, then
quantum particles appear to be inherently predicationally incom-
plete.
5
A quantum particle subject to quantum indeterminacy seems to
PHYSI CAL ENTI TI ES 203
have either one predicational gap in its property cluster or the other,
lacking either a specific physical spatiotemporal location or a specific
instantaneous momentum. If so, it is hard to see how we could
consider quantum physical entities as maximally consistent, predica-
tionally consistent and complete, for by virtue of being subject to
quantum indeterminacy they appear to be inherently incomplete.
The ultimate metaphysical as well as scientific interpretation of
quantum indeterminacy is contested, and its applied ontological
implications, whatever may be at stake for a preferred existence
domain, should be obvious even if the argument is inconclusive. If
quantum indeterminacy were deemed to involve a predicational
incompleteness in a physical entity, and hence to entail the entity’s
submaximal consistency, then it is not the existence of quantum
phenomena that would have to go, but rather the combinatorial analy-
sis of existence as maximal consistency. We consider the problem of the
ontology of quantum phenomena and hence of physical entities
generally in light of the quantum indeterminacy principle as a topic for
the concept of being as maximal consistency and not as a threat to the
ontological status of the microphysical and by extension macrophysical
world. What should we say about quantum indeterminacy in connec-
tion with the combinatorial analysis of being as maximal consistency?
Suppose that we do not interpret quantum indeterminacy idealisti-
cally as a mere epistemic limitation that prevents the simultaneous
determination of quantum position and momentum. If quantum
indeterminacy is not only a limitation of knowledge, but a deep
metaphysical incompleteness in microphysical reality, then we might be
faced with the prospect of having to disavow the definition of being as
maximal consistency at least of (quantum) physical entities. The
potential force of the problem is evident, but how serious is the
difficulty? The answer depends on how we understand the predica-
tional completeness requirements of quantum phenomena considered
as a specific subcategory of physical entity.
If we think of quantum phenomena as having the same kind of
existence conditions as macrophysical entities, such as tables and
chairs and galaxies, and if, again, we adopt a realistic non-epistemic
interpretation of quantum indeterminacy, then there may be no
avoiding the conclusion that, according to the combinatorial analysis
of being as maximal consistency, quantum phenomena do not, and
perhaps causally or even logically cannot, exist. This is evidently a
counterintuitive result to be avoided if at all possible. We are not
inevitably saddled with such a conclusion, if we think of the existence
conditions for predicational completeness of quantum phenomena
204 ONTOLOGY
somewhat differently than in the case of ordinary macrophysical
physical entities. We can do so with good conscience, for example, if
we regard quantum physical entities as predicationally complete if
either but not both their position and momentum are precisely deter-
minable at any instant of real time. We can say, in other words, that
quantum physical entities are predicationally complete, in the only
way that spatiotemporal entities of their kind can possibly be com-
plete, when either their position or momentum is determinable.
The problem of human choice and intervention in the verification
of a quantum particle’s properties is a widely discussed aspect of
quantum indeterminacy. It seems to make the propertyhood of a
quantum entity a function of what cognitive agents choose to do.
Shall we test a quantum particle for its position rather than its
momentum, or alternatively try to establish its momentum rather
than its position? We can readily imagine, prior to either decision on
the part of a quantum physicist investigating the properties of a
quantum particle, that if it were decided to check the particle’s pos-
ition then it would indeed have a position to be discovered, while if
alternatively it were decided, counterfactually under the circum-
stances, to check the particle’s momentum, then equally the particle
would have a momentum to be discerned. The joint determinability
of position and momentum of a quantum physical entity prior to the
successful effort even in theory to determine one or the other
property should be sufficient, other things being equal, on the combi-
natorial analysis of being as maximal consistency, to maintain that a
quantum particle exists at least until a physically interactive interven-
tion is undertaken to assess alternatively its position or momentum.
What happens, then, at the fatal moment, when an investigator
chooses to determine a particle’s position rather than momentum, or
its momentum rather than its position? What difference can it make
to the ontological integrity (or lack thereof) of the particle, based on
its predicational completeness (or lack thereof), regardless of what a
scientific enquirer might choose to do or not do? One scenario is that
in which a quantum particle is spinning merrily along, predicationally
as complete and maximally consistent in all its property combinations
as you please until a meddling researcher intervenes with a procedure
to verify alternatively the particle’s position or momentum, at the
precise instant of the consummation of which the particle becomes
predicationally incomplete and hence submaximally consistent, and
so passes instantly from existence into nonexistence. The trouble with
this interpretation is that it ignores the apparent scientific conviction
that a particle persists through the operation, albeit a particle that did
PHYSI CAL ENTI TI ES 205
not at the moment of enquiry have both position and momentum as
equideterminables, and that consequently cannot be precisely
reidentified, but whose spatiotemporal career is at most statistical.
6
Without applying these conclusions to the problem of whether the
realistic versus idealistic or epistemic interpretation of quantum inde-
terminacy is correct, we can draw further conclusions about the
nature of quantum phenomena in applied scientific ontology. We can
reasonably speculate within a combinatorial framework that the
quantum particle does not disappear from existence the instant its
position or momentum is verified, because, as we have already
suggested, a quantum particle, unlike a macrophysical physical entity,
might not simultaneously need to have both position and momentum
in order to be predicationally complete. Analogously, a macrophysical
entity does not need to be simultaneously solid and liquid in order to
be predicationally complete, provided, depending on the physical
nature of the entity, it is one or the other, and has generally the poten-
tial for either possibility, even if some entities by comparison are
simultaneously both solid and liquid at different times or in different
proper physical parts. If quantum particles do not simultaneously
have determinate position and momentum, then quantum phenom-
ena are not physically determined, just as quantum theory maintains.
The situation is not so different with respect to the particle–wave
duality exhibited by quantum phenomena and other microphysical
entities. If a quantum particle, unlike other types of physical entities,
is not supposed to be simultaneously determinable in position and
momentum in order to be predicationally complete, then it can hardly
be faulted as predicationally incomplete when a probe of its position
makes its momentum inaccessible or even indeterminable, or the
reverse. If a quantum particle, given the kind of physical entity it is, is
not supposed to have simultaneously both determinable position and
momentum, then it cannot responsibly be judged predicationally
incomplete when by virtue of quantum indeterminacy it turns out
only to have one property or the other, but never both at the same
time. Macrophysical entities, in contrast, appear to be a totally differ-
ent kettle of fish, although their macrophysical properties and ontic
status presumably depend in some way on their microphysical proper-
ties. They might need to be predicationally complete by virtue of
always possessing simultaneously determinable position or centre of
mass and momentum. That discrepancy, however, should perhaps be
understood metaphysically in the end as testimony to the differences
in the physical properties of quantum and macrophysical entities.
Abstract entities, particular and
universal: numbers, sets, properties,
qualities, relations, propositions
and possibilities, logical,
9 mathematical and metaphysical laws
Abstract entities
More ink has been spilled on the question of the existence of abstract
entities than on any other topic in ontology. Do universals exist?
What about sets and numbers, properties, qualities, relations, propo-
sitions and laws? What light can we shed on these controversies from
the standpoint of a combinatorial analysis of being?
We have already touched on several categories of abstract entities.
Looking forward to what might be said or what others have said about
non-spatiotemporal particulars and universals, we have provisionally
considered the possibility of their existence. We must now put our
cards on the table and examine whether in fact there are abstract
entities, whether abstract non-spatiotemporal things in addition to
physical spatiotemporal things exist, and whether or not abstract
entities should be included in the extant or preferred theoretical exist-
ence domain.
The fact that the combinatorial analysis provides a definition of
what it means for something to exist gives us an important advantage
over most of the history of metaphysics in which the ontic status of
abstract entities has been debated. Without a clear-cut positive
concept of being, applied scientific ontology can only fumble in the
dark, relying on Ockham’s razor to determine whether or not a
purported unperceivable entity exists according to perceived minimal
explanatory needs. As we noted in our critique of Quine’s criterion of
ontological commitment, Ockham’s razor is an uncertain basis for
deciding what actually exists. We must decide what we think we need
to explain or not explain, and whether we can offer good enough
explanations that do or do not presuppose the existence of a certain
category of putative entities. If we think we need to posit such enti-
ties, then, presto, they exist. If, upon due consideration, we conclude
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 207
that we do not absolutely need such putative entities after all, then,
supposedly, they do not exist. This, one might say, is enormous onto-
logical largesse, depending for its conclusions on potentially conten-
tious conceptions of what needs to be explained and what is to count
as an adequate explanation. Are these the kinds of considerations that
ought to make or break the existence of an entity?
In our reflections on the requirements of a preferred existence
domain thus far, we have followed a different method. We have
thematized and brought forward for more self-conscious philosophi-
cal examination the problem of what it means for something to exist,
just as Heidegger, our beacon in his statement of the fundamental
problems if not the solutions of pure philosophical ontology, says we
should. In the end, we have arrived at radically different conclusions
than Heidegger’s, substituting an Aristotelian (early) Wittgensteinian
combinatorial theory of being based on pure logic for Heidegger’s
Kantian (later) Husserlian existential theory of being based on
transcendental phenomenology.
We can still go astray in trying to apply the combinatorial analysis of
being to the unique problems posed by existence claims and counter-
claims for abstract entities, as we can at any step along the way in trying
to determine the ontic status of other kinds of other candidate entities.
The availability of a positive concept of existence, which the combina-
torial analysis affords, nevertheless makes it possible to adjudicate
disputes about the extant domain in specific terms according to the
requirements of the definition, to decide whether or not abstract enti-
ties exist on the basis of whether or not they are maximally consistent,
rather than in the more slippery contentious terms of Ockham’s razor.
At the same time, the enquiry provides an opportunity to test and if
necessary correct the proposal that being generally and in the case of
putative abstract entities is predicational maximal consistency.
Ockham’s razor versus combinatorial ontology
An excellent place to begin considering the problem of abstract
entities is with the question of their usefulness and explanatory
convenience in mathematics, science, philosophy and other fields of
discourse. The utility of being able to appeal to abstract entities is
virtually unchallenged even by the most staunch opponents of their
existence. Honing Ockham’s razor to eliminate them from applied
ontology, these critics have held that despite their usefulness abstract
entities are not strictly needed for the kinds of explanations we
strictly need.
208 ONTOLOGY
Since we have already found reason to doubt the universal applica-
bility of Ockham’s razor, we shall not try to make this strong condition
a general requirement for the existence of abstracta. The decisive issue
for our purposes is instead the question of whether or not putative
abstract entities satisfy the combinatorial analysis of the concept of
being; whether or not, that is, putative abstract entities are predica-
tionally maximally consistent. If so, then irrespective of current
impressions of their explanatory necessity or superfluity, we shall
conclude that they exist. If not, if putative abstract entities are either
predicationally inconsistent or predicationally incomplete, then, despite
the most convincing considerations in support of their explanatory
indispensability, we shall provisionally conclude from the current state
of argument that they do not exist. If necessary, we will at least provi-
sionally leave some kinds of explanations we may think we require bereft
of the corresponding entities we may think the explanations require.
We thereby avoid assumptions about the status of contemporary
expectations for good explanations involving putative abstract
particulars or universals. If abstract entities satisfy the requirements of
the combinatorial analysis of being, and are judged to exist, but are not
thought to be necessary for any of the kinds of explanations we now
believe ourselves obligated to provide, then we shall hold open the
possibility for their future explanatory use. If abstract entities fail to
satisfy the requirements of the combinatorial analysis of being, and are
judged not to exist, but are believed to be explanatorily necessary, then
we hold out the prospect of rethinking our current evaluation of what
we need to explain, or of what should count as an adequate explanation,
leaving the issue of whether the explanations we are truly obligated to
give truly need to make reference to abstract entities.
We observe that assessments of whether or not abstract entities are
needed for explanations have varied historically according to the
kinds of explanations that have been favoured at different times and
in different cultural contexts, and in the future will undoubtedly
continue to vacillate. Perceptions of explanatory obligations are
subject to what Thomas Kuhn in The Structure of Scientific Revolu-
tions portrays in the ongoing sociology of scientific explanation as
paradigm shifts. Abstract entities, if they exist, must be eternal,
changeless, timeless, by virtue of being non-spatiotemporal. We note
that putative abstract entities have generally been dismissed from the
preferred theoretical existence domain of an applied scientific ontol-
ogy whenever they could be shown either to be predicationally incon-
sistent or incomplete, or both, but that many other putative abstract
entities have stood the test of time and emerged as prima facie
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 209
maximally consistent, as having or being constituted by maximally
consistent property or states-of-affairs combinations, and hence,
according to the combinatorial analysis, actually existing.
Particular and universal abstracta
It is worth taking stock of a subdivision in applied ontologies that
countenance abstract entities. This is the distinction between particu-
lar and universal abstracta. Roughly, numbers, sets and propositions
are assumed to be abstract particulars, even if they admit of universal
applications, while properties, including qualities and relations, are
usually thought to be universals, despite the fact that each considered
in its own right is also in a clear sense a particular entity, distinct from
other abstract things.
The number r, for example, seems as much an individual entity, if
it is one at all, as the Eiffel Tower or the lucky arrowhead in my
pocket, albeit of an ontologically different kind. It is a particular
number along the number line with a host of distinguishing proper-
ties, including being irrational, involving an indefinite decimal expan-
sion of digits beginning 3.14159 . . ., and many others besides. The
putative abstract universal entity red or redness, if there is such an
existent abstract entity, in contrast, is commonly characterized as a
universal, a quality that all particular red things alike exemplify,
instantiate, or in which they participate, or that can hold true of
indefinitely many particular red things. Red or redness is also in
another sense itself a particular thing, a particular universal, for it is
not blue or bashful or triangular or any other distinct quality or rela-
tion; it is a particular colour, redness or red, and not another univer-
sal. The same is true on reflection, even if we ascend to the top of the
universals hierarchy and consider just the universal universal.
1
The fact that some of these entities include spatiotemporal proper-
ties in their maximally consistent property combinations and others
do not, does not ontologically privilege one category of existent
entity over any other in a combinatorial ontology. If putative abstract
entities are maximally consistent, then they exist; for in that case they
as fully satisfy the logical combinatorial requirements of being as any
actual physical entities existing in real spacetime. We may have a soft
spot in our hearts for spatiotemporal entities, since we are such
entities ourselves and we ordinarily have immediate sensations of
them whenever we are conscious. In a combinatorial pure philosophi-
cal ontology, on the other hand, there is no justification for ontologi-
cal prejudice in favour of physical over abstract entities.
210 ONTOLOGY
The only relevant question is whether the putative entities under
consideration are or are not maximally consistent. Then whether
their property combinations include or fail to include spatiotemporal
properties is no more decisive than whether their property combina-
tions include or fail to include any other category of property or prop-
erty complements. Being in a combinatorial analysis is one thing, as
Parmenides rightly believed. Contrary to Parmenides, however, as
Aristotle rightly believed, being is made up of many different kinds of
beings, of real existent physical and abstract entities in complicated
interrelations of real existent physical and abstract states of affairs in
the actual world. It is as much a fact about triangles that their interior
angles sum to exactly 180° as it is that you can boil water at sea level
at 100° on the surface of the Earth, even though water is a
spatiotemporal physical substance, and triangles are not, and the
degrees of angles in geometry are not the same kind of thing as the
degrees of a physical entity’s temperature.
The burden of proof in such an analysis shifts to opponents of the
existence of abstract entities either to refute the combinatorial analysis
of being, or to argue convincingly that putative abstract entities are logi-
cally inconsistent or predicationally incomplete. It remains an open
possibility, at this stage of our deliberations, whether a strong philo-
sophical argument can be raised against the maximal consistency of
abstract entities. If abstract entities, especially numbers, sets, properties,
qualities, relations, propositions and any others that lubricate our ex-
planations of phenomena, in combination with physical entities, play
a useful role in discourse, then why not theorize that they exist – unless
or until a good reason surfaces to question their consistency or com-
pleteness? Why not give them the ontic benefit of the doubt?
Third man argument
A celebrated objection to the existence of universals is the so-called
third man argument. Universals are supposed to be real existent prop-
erties corresponding to the predicates by which the condition of an
object is qualified. In Plato’s theory of Forms, universals are posited as
the abstract archetypes of particular perceivable things. If Joe and
Mary and Jill are human, then Joe and Mary and Jill can all be said to
exemplify or instantiate or participate in the universal humanity or
Platonic Form of the ideal man.
The third man objection states that positing the existence of
universals or Platonic Forms runs foul of Ockham’s razor. If we
suppose that individual flesh and blood human beings (the first man
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 211
or multiple men) instantiate the Form of man or universal humanity
by virtue of the universal being itself a human being (second man),
then there must be another higher order Form or universal instanti-
ated by all individual flesh and blood human beings and the universal
they instantiate (third man). And so on to infinity. Presumably,
however, the objection continues, we have no explanatory use for any
of these higher universals beginning with the third man, beyond at
most the lowest level universal of humanity or Form of man in the
series, which is to say the second man.
2
Ockham advises us to shave Plato’s unruly growth of beard right
from the start by disallowing even the first universal ideal man, and
adopting instead a nominalistic account of multiply instantiated
properties. Aristotle forestalls the infinite regress of the third man
without giving up at least such universals as inhere in existent particu-
lars, in effect by denying that the ideal man is a man, or that white-
ness is itself white. This is enough to block the regress, which cannot
get off the ground without the assumption that universals themselves
have the property exemplified by their instances. If we are not
uncritically committed to Ockham’s razor, then the explanatory
inutility of higher orders of universals may not matter to us anyway.
Finally, combinatorial ontology does not guarantee the existence of a
universal instantiated by the members of every random collection of
entities. If the ideal man is not itself a man, then, as in Aristotle’s
solution, the regress cannot get started. Since universals are supposed
to be abstract entities, they do not constitute additional instances of
the particular individuals that instantiate them. Thus, there is no
argument for extending their inclusion in higher and higher orders of
greater more comprehensive universality. If we do not apply
Ockham’s razor uncritically, then the third man argument does not
offer a good reason for excluding abstract entities from a preferred
existence domain.
Berkeley’s objection to abstract ideas
It is significant for the truth of the combinatorial analysis that challenges
to specific subcategories of abstract entities or to the very idea of a non-
spatiotemporal non-physical entity generally be conducted on the
grounds that the entities in question are either predicationally inconsist-
ent or incomplete. If there is a presumption of both the usefulness and
maximal consistency of abstract entities, then we can begin to consider
criticisms of their existence. Such an attack against the idea of an
abstract general object that goes beyond facile appeals to Ockham’s
212 ONTOLOGY
razor is mounted by Berkeley and approved by Hume as discrediting the
possibility of abstract general entities.
Berkeley’s argument offers phenomenological evidence, perfectly
appropriate in applied scientific as opposed to pure philosophical
ontology, for the conclusion that the concept of an abstract entity
precludes its existence, on the grounds that an abstract general object
is inherently predicationally incomplete. Thus, in A Treatise on the Prin-
ciples of Human Knowledge (1710), Berkeley states:
If any man has the faculty of framing in his mind such an idea of
a triangle as is here described, it is in vain to pretend to dispute
him out of it, nor would I go about it. All I desire is, that the
reader would fully and certainly inform himself whether he has
such an idea or no. And this, methinks, can be no hard task for
any one to perform. What more easy than for any one to look a
little into his own thoughts, and there try whether he has, or can
attain to have, an idea that shall correspond with the description
that is here given of the general idea of a triangle, which is,
neither oblique, nor rectangle, equilateral, equicrural, nor
scalenon, but all and none of these at once?
3
It may appear that Berkeley’s thought experiment concerns only
abstract individuals, represented here by “the triangle” as a specific
particular abstract entity. The context and its usual interpretation and
application by other critics makes it clear that the same argument is
supposed to apply with equal force to such universals as triangularity,
or any other type of properties, qualities or relations.
Berkeley’s criticism of abstract general ideas and his counterproposal
for the interpretation of what is called abstract reasoning without on-
tological commitment to abstract entities prompts Hume in A Treatise
of Human Nature (1739–40) to proclaim Berkeley’s refutation as “one
of the greatest and most valuable discoveries that has been made of late
in the republic of letters”.
4
In An Enquiry Concerning Human Under-
standing (1748), Hume further offers his own version of Berkeley’s
refutation of abstract general ideas in connection with his objections to
the possibility of the infinite divisibility of extension:
An extension, that is neither tangible nor visible, cannot possibly
be conceived: and a tangible or visible extension, which is neither
hard nor soft, black nor white, is equally beyond the reach of
human conception. Let any man try to conceive a triangle in
general, which is neither Isoceles nor Scalenum, nor has any
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 213
particular length or proportion of sides; and he will soon perceive
the absurdity of all the scholastic notions with regard to abstrac-
tion and general ideas.
5
Berkeley’s argument has convinced many a sceptic of the impossi-
bility of there existing abstract general ideas that could possibly satisfy
the predicational completeness required of an actually existent entity.
If, as Berkeley contends and Hume applauds, abstract general entities
are inherently predicationally incomplete, then they do not exist
according to the combinatorial analysis of the concept of being.
Berkeley’s refutation of abstract general ideas is inconclusive, and
does not show that abstract entities are inherently predicationally
incomplete. The failure of Berkeley’s argument, supposing the objec-
tion convincing, by itself does not establish the maximal consistency of
abstract entities, or their existence. It can at best remove one major and
historically influential obstacle to the possibility that abstract general
objects exist, and to that extent militate against the realist view that
some and perhaps even all abstract entities belonging to traditional
categories actually exist. The solution to Berkeley’s objection must be
similar to the distinctions drawn in order to rescue microphysical
entities from the charge of predicational incompleteness extrapolated
from dilemmas about the position-or-momentum indeterminacy of
quantum phenomena. The suggestion is that abstract entities are not
predicationally incomplete in the way that Berkeley maintains because
entities of the relevant kind are not supposed to have any of the prop-
erties or their contraries that Berkeley mentions in order to be
predicationally complete.
Where perceivable properties are concerned, it is easy to defend
the concept of the triangle as an abstract general entity lacking any
colour. The argument is that mathematical entities like the triangle, if
they exist, are non-spatiotemporal, and as such cannot enter causally
into the chromatic absorption and reflection of light waves of any
frequency that constitute colour, nor can they be perceived by colour-
sensitive subjects. The triangle is no more supposed to have colour
than the number 2. Similarly, then, an adequate idea of the triangle
should not be expected to have any colour. The abstract mathematical
properties Berkeley lists are less obviously irrelevant to the predica-
tional completeness or maximality of a mathematical entity like the
triangle, but the problem there is no different. It is no more incum-
bent on the abstract entity the triangle to be either isosceles or scalene
than it is for the abstract number 2, or than it is for the triangle or for
an isosceles or scalene triangle to be even or odd, or prime or divisible
214 ONTOLOGY
without remainder by numbers other than 1 or itself. The number 2 is
just not that kind of thing. Nor is the triangle that kind of thing. The
predicational completeness or incompleteness of these entities does
not depend on their having any of these particular properties or their
contraries. To imagine otherwise amounts to what Gilbert Ryle calls a
category mistake in Berkeley’s argument.
6
There is also an important logical distinction that Berkeley’s objec-
tion overlooks. It is no mark against the predicational completeness,
and hence no detraction from the existence, of an inanimate physical
entity like my bicycle that it is neither happy nor unhappy. A bicycle,
lacking any psychology, is just not the sort of thing to support either
of these properties or their contraries. The bicycle is predicationally
complete even if it is neither happy nor unhappy, miserable nor joyful,
nor capable of experiencing any other emotion. A physical entity, on
the other hand, in order to exist, according to the combinatorial
analysis of being, must either be happy or non-happy. My bicycle is
non-happy, but not unhappy. In order to be unhappy, my bicycle
would have to be capable also of being happy, which I sincerely doubt.
A nonexistent bicycle in a work of fiction, on the other hand, would
be incomplete in one among innumerable ways were it not specified
as being either happy or non-happy, neither unhappy nor non-
unhappy, neither having nor failing to have a humanlike internal
emotional psychology, as inanimate real-world objects in fairy tales
are sometimes described as possessing.
The distinction between un- (contrary) and non- (contradictory or
complementary) properties is not unique to modern symbolic logic. It
is incorporated already in propositional form in the more classical
Aristotelian syllogistic logic with which Berkeley and Hume would
have been familiar. We find it explicitly in the difference between
contraries and contradictories, as between contrary and contradictory
categorical predications, in the traditional square of opposition.
Berkeley is right to insist that abstract entities are often not the true
predication subjects of many choices of contrary properties. More
significantly, though, Berkeley is wrong in thinking that abstract
general entities are not the true predication subjects of any chosen
pairs of contradictory or complementary properties, and, equally
importantly, he would be utterly mistaken in assuming that an entity is
predicationally incomplete merely by virtue of lacking all contrarily as
opposed to contradictorily or complementarily opposed properties
within their respective constitutive property combinations.
The same considerations apply with respect to the predicational
completeness or incompleteness of the property combinations that are
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 215
supposed to constitute the putative abstract entities whose ontic status
Berkeley considers. It is no detriment to the predicational completeness
of the triangle that it is neither black nor white nor red nor blue nor
green nor yellow, or that it is neither isosceles nor scalene nor of any
other specific triangular shape, beyond consisting of three angles joined
by three line segment sides. It would, on the other hand, very much
undermine the predicational completeness and hence the existence of
the triangle on the combinatorial analysis of being, if Berkeley were to
show that the triangle is neither black nor non-black, neither white nor
non-white, and so on; or, in general, that it is neither coloured nor non-
coloured. The triangle as an abstract mathematical non-spatiotemporal
entity is definitely non-black, definitely non-white and so on, because
it is definitely non-coloured. It is the same, although perhaps less
obvious, with respect to the properties of having a specific shape, such
as being isosceles or scalene. The triangle, as the particular kind of
abstract entity it is supposed to be, would be altogether nonexistent if
it were neither isosceles nor non-isosceles, neither scalene nor non-
scalene, or having neither any specific shape nor its contradictory or
complementary property. The counter-objection to Berkeley is that the
triangle is definitely non-isosceles, non-scalene and so on, and thus
suffers no predicational incompleteness.
As to ideas or mental images of abstract entities, Berkeley is right
that they can only be particular in their predicationally complete
properties, like a physical representation such as a drawing or paint-
ing or model, and hence an inadequate ideational depiction of an
abstract universal entity. Berkeley is therefore correct to say that, if we
are going to think of a triangle in the sense of holding a corresponding
image in mind, then phenomenologically we can only do so by conjur-
ing up a particular triangle with a definite shape, and, what is more, a
definite colour, among other definite features, before the mind’s eye.
The particular triangle image, as Berkeley argues, is at least momen-
tarily delegated to represent the class of all triangles. The particular
choice of a type of triangle to be held up to the imagination for these
very reasons is thereby guaranteed inadequately to picture the
concept of the triangle in general as an abstract entity. The inference
to draw from this fact, however, is not that abstract entities do not
exist, but that they cannot be adequately imagined. Berkeley and
Hume regard this limitation of mental imagery as sufficient proof that
the triangle does not exist, and that by implication all putative
abstract general entities do not exist. The consequence, nevertheless,
follows only for thinkers like Berkeley and Hume who assume that an
entity exists only if we can have an adequate idea of it, phenomeno-
216 ONTOLOGY
logically in the sense that the idea is ultimately related to originating
sensations. In Hume’s terminology, the idea of an existent entity must
originate as an impression of sensation or reflection. Overlooking
crucial differences for the sake of emphasizing something they hold in
common, Berkeley’s and Hume’s self-consciously humanized empiri-
cism in this respect more closely resembles Heidegger’s dependence
on phenomenology in existentialist ontology. We have made no such
assumption, and so we are not bound by its limitations. We are not
committed to empirical introspective or phenomenological methods
in trying to determine the existence of entities, but are relying instead
on logical foundations in a combinatorial ontology.
Numbers and sets
We can, accordingly, deal briefly but decisively with what is otherwise
a vexed question in applied ontology concerning the ontic status of
mathematical entities. The problems here notably concern the existence
or nonexistence of numbers and sets, but also geometrical objects like
the triangle, considered as abstract particulars. The combinatorial
analysis of being implies that mathematical objects exist, not if and only
if they are needed in order to explain something else whose existence
in another context might equally be subject to doubt, but, instead, if and
only if they are predicationally maximally consistent.
Mathematical entities, although they seem in some sense to be
things, cannot be directly perceived in order to verify their existence
as entities. That, naturally enough, is why philosophical controversies
about the existence or nonexistence of abstract objects, especially
mathematical entities that seem to be so indispensable to our under-
standing and application of the sciences, continue to rage. It is also
why the philosophy of mathematics is so persistently preoccupied
with heated arguments for and against the ontological reduction of
numbers to sets or sets to numbers or other mathematical particulars.
If we could simply see abstract entities, we would not need to dispute
their existence or nonexistence.
7
Without trying to prove that mathematical entities are absolutely
required for explanatory purposes, having relaxed the demands of
Ockham’s razor, we can rely on the evident usefulness of numbers and
sets and other mathematical particulars and universals in accounting for
truth in mathematics and the sciences. Additionally, formal mathemati-
cal metatheory proves the consistency and completeness of many
specific mathematical languages. Typically it does so by applying meth-
ods of mathematical induction to establish the possibility of a model for
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 217
the systems, in which all the axioms and theorems of the language are
interpreted as true. Although consistency and completeness cannot be
jointly proved in the case of some of the most interesting formalisms,
such results, at least where available, provide further partial evidence
of the maximal consistency of the abstract mathematical entities posited
by the propositions of demonstrably consistent and complete
mathematical theories. The effort to certify mathematical systems as
syntactically consistent and deductively complete in turn signifies a
recognition in metamathematics of the equivalent of the combinatorial
analysis of being as maximal consistency with respect to the existence
conditions of abstract mathematical entities defined by the axioms and
theorems of a mathematical system.
We can say all that needs to be said under the circumstances by main-
taining provisionally that there is a strong presumption in favour of the
maximal consistency, and hence existence, of numbers and sets, accord-
ing to the combinatorial analysis of being, unless or until a sound
objection to their predicational consistency or completeness is pro-
duced. We have already considered two criticisms of the existence of
abstract entities, that, if successful, would have had immediate negative
implications for the existence of mathematical entities. The third man
argument invokes Ockham’s razor in an effort to eliminate universals
from the ontology, while Berkeley’s thought experiment concerning the
triangle as an abstract mathematical particular purports to show that
there can exist no abstract general ideas. If our counter-arguments are
correct, then both of these objections fail. If the third man and
Berkeley’s thought experiment are the most powerful but still indeci-
sive criticisms to be considered, then the presumed maximal consistency
of mathematical entities can at least tentatively be upheld. We thereby
satisfy the combinatorial requirements for conditionally including
mathematical objects as existent abstract entities, shifting the burden of
proof to deny their existence to the opposite side of the controversy, to
be met if possible by sceptics and nominalistically minded opponents of
the existence of numbers, sets and other abstract mathematical entities.
We shall later engage the problem of ontological reductions of
numbers to sets or sets to numbers, or to other mathematical, abstract,
or even non-abstract, spatiotemporal entities, in more depth. For the
moment, it suffices to remark that if numbers and sets are useful, even
if not absolutely explanatorily indispensable, and if there are no
knockdown objections to the predicational consistency or complete-
ness of abstract mathematical entities, then we shall consider
ourselves entitled in the interim to consider both numbers and sets,
along with related abstract mathematical particulars and universals
218 ONTOLOGY
with the same qualifications, to exist as truly and fully and in the same
sense of the combinatorial concept of being as any existent physical
spatiotemporal entity.
Properties, qualities, relations
The situation is much the same with respect to the ontic status of
properties, qualities and relations as with mathematical entities.
There is a presumption in favour of the existence of useful even if not
absolutely indispensable putative abstract entities in this category.
There is also a comparable battery of objections to their existence,
which we have already tried to answer, and which are generally
variations on the themes of the third man or other applications of
Ockham’s razor or Berkeley’s thought experiment. There is an exten-
sive philosophical tradition of efforts to reduce one subcategory of
abstract entities to another, usually offered in league with appeals to
Ockham’s razor.
Such similarities justify extending the same basic argument in
support of the existence of abstract properties, qualities and relations
that was previously considered in trying to establish the ontic status of
mathematical particulars. We locate the burden of proof with those
who want to challenge the existence of universals, acknowledging
that we have yet to entertain a convincing objection to their
predicational maximal consistency. An interesting twist for this
category of putative abstract entity is that we now finally have the
opportunity to address the problem of the ontology of the properties,
which we previously regarded as ontically neutral logically possible
properties in the combinatorial analysis of being. In a sense, this ques-
tion is no different than that of the ontic status of logically possible
objects as the bearers of logically possible properties in logically
possible states of affairs. We have already made partial progress con-
cerning their existence in understanding the ontology of physical and
abstract entities in the subcategory of abstract particulars. All these
issues are intimately interconnected, since logically possible objects
can be understood as property combinations, and properties can be
understood as objects that themselves have higher-order property
combinations by which they are defined.
It is standard to regard properties as the more general category
subsuming qualities and relations, and to equate properties of either
subcategory as abstract entities with universals. The difference between
qualities and relations is at least superficially that qualities are one-
place properties, like the property of being red or being happy, and
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 219
relations are more-than-one-place properties, like being the sister of
someone, or being taller than the father of the President of the United
States. It is sometimes proposed as an obvious simplification of these
distinctions that properties be thought of as limiting cases of relations,
or that relations be construed as relational properties. To reduce quali-
ties to relations, a variety of devices for abstracting properties from
relations are proposed in symbolic logic, all of which amount more or
less to the intuitive idea that we can concatenate the terms of the
relation, such as being the sister of May, into the one-place property
form, being-the-sister-of-May, and predicate that property, say, of June,
so that June then has the one-place relational property of being-the-
sister-of-May. We shall follow only the first of these conventions here,
recognizing that properties subsume qualities and relations. In
contrast, we will no more consider ourselves obligated to reduce quali-
ties to relations or relations to qualities than we are to reduce numbers
to sets or sets to numbers.
The ontic status of properties should now be clear. We provision-
ally accept them as existent entities on the grounds of their extraordi-
nary usefulness in explaining a large variety of phenomena, in lieu of
serious objections to the presumption that they are predicationally
maximally consistent. The properties in property combinations we
have previously spoken of only in an ontically neutral way, as logically
possible properties, can now be considered to exist as truly and fully
and in the same combinatorial sense as the existent objects we have
already commended as physical or abstract individuals. We conclude,
in other words, that universals exist, provided they are themselves
predicationally consistent and complete. This is not to say that all
putative universals exist, since many candidates for inclusion in the
preferred existence domain, like many nonexistent objects, will need
to be excluded on grounds of predicational incompleteness or incon-
sistency. In particular, putative universals, properties, qualities or
relations that give rise to logical paradoxes must be eliminated from
the ontology on grounds of predicational inconsistency. An obvious
representative example is the nonexistent property postulated by the
so-called barber paradox, of being a barber who shaves all and only
those persons who do not shave themselves, /x[œy[Sxy ÷
-
Syy]].
8
A
large part of the importance of trying to uncover logical and other
types of conceptual paradoxes in philosophy and logic has as its
motivation the testing of putative universals to see if they stand the
test of predicational maximal consistency. We ask, in effect, whether a
theory gives correct necessary and sufficient conditions for the
concept of an abstract object or property. A sustainable antinomy
220 ONTOLOGY
concerning a putative abstract entity is a bad mark against it. If the
candidate cannot be defended against objections to its consistency or
completeness, then its proponents should in all honesty give up their
commitment to its existence and admit that there is no such entity.
Maximal consistency is a requirement that not all putative properties
can satisfy, even among those that have otherwise been thought to be
highly useful in philosophy, mathematics and the sciences.
Do we not, finally, face a vicious circle or infinite regress in this
treatment of the ontology of universals? We say that a property has
being if and only if its property combination is predicationally
maximally consistent. To answer this question affirmatively, we must
presumably ask whether the properties in a property’s property
combination are themselves existent, which requires in turn that their
higher-order property combinations be predicationally maximally
consistent. We may reel at the dizzying prospect of these seemingly
endless ramifications of the combinatorial analysis of being. Can the
existence requirements of properties, and hence of logical objects,
ever be resolved or come to a definite conclusion? Can the existence
of anything whatsoever be grounded firmly in pure philosophical or
applied scientific ontology? Are we doomed to going round and
round in yet another version of Heidegger’s circle?
The situation, luckily, is not so desperate. The problem is important
and must not be evaded, but there is a straightforward solution. An
infinite regress or vicious circle does not arise if there are properties
that do not happen to involve any internal predicational inconsistency
or incompleteness. How we are to know whether and which particu-
lar properties meet these intuitive qualifications is a topic for episte-
mology rather than metaphysics. We do not need to guarantee that
there are maximally consistent properties at ground level in ontology.
We need not posit, as philosophers for other reasons have sometimes
done, that there must ultimately be basic, primitive or irreducible
indefinable properties. Such properties at the foundations of our
conceptual scheme are supposed to be logically and conceptually so
elementary that they afford no occasion for internal predicational
inconsistency or incompleteness. It is instead a logically necessary
consequence of the combinatorial analysis of being that there must be
predicationally maximally consistent properties, because among all the
logical possibilities there must be at least some maximally consistent
combination of the logically possible properties of logically possible
properties. With these building blocks, whatever they turn out to be,
we can then in principle explain the existence of all other existent
properties and all other existent entities. If it is true that universals are
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 221
existent abstract entities, then the properties that intrinsically satisfy
the combinatorial existence requirements are not merely logically
contingent, but must be identically constituted and hence exist alike in
every logically possible world.
9
The combinatorial analysis of being also decides the historical
dispute between Plato’s realism and Aristotle’s inherentism. The main
distinction between Plato’s and Aristotle’s theories of universals is
that Plato regards Forms or Ideas as existing independently of the
ontic status of any of their instances, whereas Aristotle argues that his
corresponding definitions and secondary substances exist depend-
ently only in so far as they inhere in actually existent physical spatio-
temporal things or primary substances. A combinatorial applied
scientific ontology of abstract entities implies that universals actually
exist, much as Plato in contrast with Aristotle holds, provided that
they are maximally consistent in their constitutive property combina-
tions. This, moreover, is a matter that can be decided defeasibly in
practice when there is good reason to believe and no good reason to
disbelieve that a putative universal property, quality or relation, is
maximally consistent. The question of whether or not a putative
abstract entity is maximally consistent considered in itself appears to
be logically independent of whether or not there happen to exist any
physical spatiotemporal entities instantiating the properties, thereby,
other things being equal in choosing between these theories, favour-
ing a Platonistic realism over an Aristotelian inherentist metaphysics
of universals.
Propositions as truth-valued sentences
The ontic status of propositions raises special problems for applied
scientific ontology. The extreme ontological alternatives with respect
to the metaphysics of propositions are a Fregean Platonism on the one
hand, and on the other a radical nominalism or inscriptionalism, in
which propositions are said to be nothing more than physical marks in
a physical medium that are causally related to language users via what
Quine, in Word and Object, describes as “stimulus-meanings” in a
behaviouristic referential semantics.
10
The advantage of construing propositions along the lines of Frege’s
Gedanken, literally “thoughts”, is that abstract entities provide a
convenient way to explain the common meanings expressed in differ-
ent languages, and hence by means of radically different sentences
and radically different inscription types. We thereby explain why
a sentence written in English can be translated, sometimes with
222 ONTOLOGY
virtually no loss of even the most subtle connotations, into other natu-
ral languages like German or Russian or Japanese or Hindi. We can
say that these distinct languages have evolved different conventions
for expressing an identical proposition as the thought or abstract
meaning of the sentences.
11
The existence of propositions has never-
theless often been perceived as a threat to an austere nominalistically
inclined applied ontology that seeks to minimize ontological commit-
ments beyond perceivable spatiotemporal physical entities, and that
looks with suspicion on putative non-physical entities unless they
prove to be absolutely indispensable to the metaphysics of the abso-
lutely indispensable explanations of contemporary science.
An argument against including propositions in the domain depends
on the possibility of explaining relevant psychological and linguistic
phenomena without appealing to the existence of the universal abstract
meanings of sentences. There have been several types of proposals for
eliminating propositions by positing another type of non-abstract
entity to accomplish the same theoretical purpose. The theory that we
shall examine involves a philosophical semantics in which propositions
are understood as nothing more than a special category of sentence that
proposes the existence of a state of affairs. Not all sentences are prop-
ositions, on this account. We exclude questions, commands and
requests, expletives, many types of exclamations, and other non-
propositional sentences. All propositions are nevertheless sentences.
Sentences are conventional expressions of thoughts in the psychologi-
cal sense, rather than in Frege’s Platonistic abstract entity sense of
Gedanken. Propositions, then, are true or false sentences.
The meanings of sentences, in contrast both with a Fregean
Platonistic semantics and a Quinean nominalistic–behaviouristic
semantics of stimulus meanings, can be explained in another way. In
later chapters we propose an alternative intentional semantics that
connects thoughts as psychological episodes with the expression of
the meanings of thoughts in sentences considered as existent
spatiotemporal physical entities in a way that is neither Fregean–
Platonistic nor Quinean–behaviouristic. The explanation requires a
more detailed scientific ontology of mind, from which standpoint the
expression of thoughts in language can be understood without the
excessive ontological riches of a Platonistic concept of proposition
nor the poverty of an eliminativist behaviourism or other radically
nominalistic theory of sentence meaning. This background will
prepare us to recognize meaning in language as a phenomenon related
to the expression of meaning in art and the manufacture and use of
artefacts, including all technologies.
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 223
The meaning of language is a function of thought and of the in-
terpersonal social reality in which linguistic among other expressive
phenomena evolve. The theory has as an immediate consequence
that there is no justification for including propositions as a special
category of abstract entities among others in a preferred existence
domain. If the theory succeeds, we can eliminate propositions as
special abstract entities by reducing them to true or false sentences
that expressively propose the existence or nonexistence of a certain
physical or abstract state of affairs. We can explain the meaning of
sentences in another way without appealing to the existence of
propositions as abstract entities that constitute the meanings of
sentences. It is no accident that we have no choice, even in formal
semantics, when we are trying to explicate the content of a prop-
osition as the abstract meaning of concrete sentences, including
those from different languages equivalent in meaning, than to
choose a particular language in which to present the supposedly
abstract general meaning the sentences convey. Thus, in the most
hackneyed example in semantic philosophy, we say that the English
sentence “It is raining”, the German sentence “Es regnet” and the
French “Il pleut” all mean (reverting now to English, in this context)
that it is raining. The philosophical situation is not improved by
shifting to German or French, or to another language altogether, say,
Turkish, Mandarin or Swahili.
There is no abstract language of abstract propositions in philosophi-
cal semantics. The only languages are those we thinkers contrive and
into which we are in one way or another linguistically socialized. In the
Tractatus, Wittgenstein sought to demonstrate the necessity of a
transcendent language of propositional symbols that would picture the
meanings of corresponding logically isomorphic states of affairs
conventionally expressed in a system of natural language signs. We
cannot avail ourselves of such a distinction, because we have argued
that there are no transcendent entities in combinatorial ontology. In his
later philosophy, Wittgenstein also gave up the concept of a
transcendent order of fact-picturing linguistic symbols. We shall, there-
fore, not try to wedge in propositions as a special subcategory of
abstract entities along with sets, numbers, properties, qualities and
relations. The reason is not, significantly, that we can reduce prop-
ositions to another category of abstract entities, for all abstract entities
exist, but because we can eliminate them from the existence subdomain
of abstract entities altogether, and compensate for their explanatory
service in other ways, by invoking already established subcategories of
entities, such as sentences and types or categories of sentences.
224 ONTOLOGY
If we do not have a clearly established need to include propositions
as existent abstract entities, and if we do not have good reasons to
believe that putative abstract propositions are maximally consistent,
then we should not include them in the ontology. The merits of this
policy in applied scientific ontology cannot be fully assessed until we
have set an alternative explanation in place and compared their
respective advantages and disadvantages. The point is that the
combinatorial analysis of being does not require us to accept the exist-
ence of any and all putative abstract entities that have been introduced
on grounds of their usefulness in scientific explanation. We can pick
and choose those we believe are justified as maximally consistent and
relatively more useful than their competitors, even if not indispensa-
ble, by applying a more refined version of Ockham’s razor, relegating
others where possible to another ontological category of non-abstract
existent entities. In the same way, we are not obligated to provide a
place in the preferred existence domain for such contested putative
entities as witches, ghosts or supernatural forces.
Ontic status of abstract laws
The final topic concerning the ontic status of abstract entities is that of
laws, especially logical, mathematical and, if there are any, metaphysi-
cal laws. These exhibit the same ambiguity as natural laws. In speaking
of laws for abstract entities, we can refer alternatively, as in the case of
laws for physical entities, either to patterns and regularities among the
appropriate types of states of affairs, actual or abstract, or to the linguis-
tic entities, sentences or propositions, by which they are expressed.
Abstract relations seem to be real enough in combinatorial ontology,
while propositions have already been shown the door. If logical, math-
ematical and metaphysical laws are relations of special kinds themselves,
structural patterns or regularities among abstract entities in logic, math-
ematics and metaphysics, then there is good reason to conclude that they
exist. If we mean by laws the propositions that express these relations,
and if propositions do not need to constitute a distinct subcategory of
existent abstract entities, but are only true or false sentences, then in this
sense there is even better reason to conclude that all laws, including
causal or natural physical laws, as well as logical, mathematical, meta-
physical and any others besides, over and above the sentences by which
they are expressed, do not exist. As such, laws can have no causal or
other necessitating influence of their own on the course of events in the
world, but serve at most a descriptive and predictive function in meta-
physics and the exact sciences.
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 225
It is the ontic status of abstract relations themselves with which we
are and ought to be concerned, and not directly with the ontic status of
their linguistic expression. The relations in question, the patterns and
regularities among abstract entities to which we have referred, can be
said actually to exist, provided the laws in question are true. The laws
in any case merely summarize the relations that obtain, logically con-
tingently but causally necessarily in the case of natural laws, logically
necessarily in the case of logical and perhaps also mathematical and
metaphysical laws, or else by appropriate modalities of their own. The
laws construed as representing a choice of relations among physical or
abstract states of affairs considered only in themselves have no agency
or compulsion to make things happen in a certain way. They only de-
scribe the fact that physical events happen or abstract entities for differ-
ent reasons are abstractly interrelated as the laws prescribe.
Against wholesale ontological reduction
We have previously remarked the legerdemain by which entities are
made alternatively to exist or not exist according to whether they are
judged explanatorily necessary or unnecessary under Ockham’s razor.
The method does not appear intuitively to be a sound basis for judg-
ing whether or not a putative abstract entity exists.
The problem is particularly difficult when we consider that whether
or not there is an explanatory need to include a putative entity in the
preferred existence domain is often a matter of the purpose of the
explanation, the intellectual historical and cultural context in which the
explanation is to be given, and the variable analytic, paraphrastic and
reductive ingenuity of individuals engaged in explanation. Whether we
really need or do not need universals or sets or classes or numbers in
order to secure the truths of logic, mathematics and the sciences is not
a simple question, but one with many subtleties. There have been and
will undoubtedly continue to be substantive philosophical disagree-
ments about whether or not abstract entities are required for different
types of explanations. We can only hope to settle limited aspects of the
problem in piecemeal fashion by looking closely at some of the particu-
lar proposals for doing away with or reducing one subcategory of
abstract entities in favour of another.
12
We can ask in this way whether numbers are sets or sets are
numbers, whether qualities are a limiting case of relations, or whether
relations are just a special subcategory of relational properties. If we
succeed at any of these reductions, then we might be said to have
trimmed-down the applied ontology of abstract entities, perhaps from
226 ONTOLOGY
four subcategories to two, and thereby accomplished an ontological
economy in the preferred theoretical existence domain. These are all
worthwhile efforts, if for no other reason than because of the clarity
they bring to the concepts of whatever entities are finally included in
a recommended applied scientific ontology. Apparent progress in these
reductive programmes notwithstanding, attempts to reduce putative
abstract entities in applied ontology are largely a waste of time, and
give the false appearance of proceeding with a philosophical or scien-
tific methodology in applied ontology only in the absence of being able
to implement a more positive analysis of what it means for something
to exist. The idea of reducing sets to numbers or numbers to sets, or
any of the other proposals for reduction of any subcategory of abstract
entities to any other within the general category of abstract entities,
lacks real ontological significance, because it does not give us a good
reason, even when the reductions succeed perfectly well on their own
terms, for concluding that the reduced abstract entity (or subcategory
thereof) does not really exist, in deference to the abstract or concrete
entity (or subcategory thereof) to which it is reduced.
The limitations of ontological reduction can partly be seen in the
fact that in many cases alternative reduction schemes are advanced
with comparable intuitive plausibility, but in opposite directions. The
prospect of reducing numbers to sets or sets to numbers is typical. If
both of these projects succeed by their own lights, what can we poss-
ibly conclude about whether sets really exist and numbers do not, or
numbers really exist and sets do not? The same problem extends to
proposals to reduce abstract entities generally to non-abstract con-
crete physical entities, in which the futility and irrelevance of efforts
at ontological reduction are even more transparent.
What we should do instead is obvious from the standpoint of a com-
binatorial analysis of the concept of being. We should include or exclude
putative abstract entities from the preferred existence domain solely on
the basis of whether or not a good argument can be made for their
maximal consistency. In doing so, we gain a new perspective on the
futility of the ancient metaphysical deadlock of realism versus nominal-
ism and all the variations in between. We discover in the process that it
is as pointless as a general strategy in applied ontology to reduce abstract
to concrete entities, whether instances, tokens of types, or tropes or
modes, parts or moments, of existent particulars. It is especially futile
in contexts of scientific explanation that rely uncritically on the prin-
ciple of Ockham’s razor. We accomplish nothing of ontic significance
by trying to decide whether numbers can be reduced to sets or proper-
ties or propositions, or propositions to properties or sets or numbers.
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 227
It is no more ontically revealing to discover that such reductions
can be achieved than to decide that pions and muons can be reduced
to quarks, or that, on a gross scale, chairs and tables can be reduced to
smaller physical constituents, and ultimately to molecules and atoms
and subatomic particles and quarks and energy fields. If we agree that
all these physical entities can be reduced to or are actually made up of
quarks, do we then want to say that among physical entities only
quarks really exist? If quarks exist, however, then, presumably, so do
all of the things that are made out of quarks and can in that sense be
reduced to quarks. If the parts of my bicycle exist, then so does my
bicycle, even if only as a scattered object when I have taken it apart.
On the proposed combinatorial analysis of the concept of being, all of
these things fully deserve to be considered existent on the assumption
that all alike equally satisfy the combinatorial requirement of maxi-
mal consistency, predicational consistency and completeness.
The same is true, pari passu, of putative abstract entities in their
part of the preferred existence domain. Again, we proceed on the
assumption that sets, as well as numbers, propositions and the like,
are each and all in their respective subcategories and in the relevant
appropriate ways maximally consistent. If it is ontologically unexcit-
ing to learn that properties are really relations of various kinds, or the
opposite, it is nevertheless potentially very instructive with respect to
our understanding the conceptual networks to which the ideas of such
putative abstract entities appear to belong. Then it is not a matter
even of applied scientific ontology, but of higher-order metaphysics
and conceptual analysis of the meanings of these terms and concepts,
which it is not a trivial matter to work out correctly. If all of these
putative abstract entities are maximally consistent in their respective
property combinations, then they exist. In that case, they have as
much reality, as much being, as the Eiffel Tower or the arrowhead I am
turning over in my fingers as I write, or your thoughts just at this
moment, or your favourite actually existent entity or physical state of
affairs, an event you cannot be made to deny exists. If all of these
putative entities are maximally consistent, then, according to the
combinatorial analysis of being, they are real actually existent entities.
There is no more need to choose one type over another as actually
existent than there is in the case of quarks and muons and gluons and
electrons and atoms and molecules and rocks and roses and rhinoceri,
planets, solar systems, galaxies and the existent states of affairs that
constitute the entire physical universe, all of which with due qualifica-
tions can rightly be said to exist. They exist, according to the combi-
natorial analysis of being, not because we believe we need them in
228 ONTOLOGY
order to make sense of prized scientific theories and because we have
thus far failed to reduce them to another more encompassing sub-
category of abstract entities or something non-abstract, but because,
in more positive terms, they are believed on the basis of reasonable
arguments to be predicationally maximally consistent, logically
coherent in their descriptions of the entities in question with no legiti-
mate property or property-complement gaps. What more could we
possibly want, especially of putatively abstract entities in a preferred
existence domain? This should be all that is required, provided we are
satisfied in the first place with the combinatorial analysis of being as
maximal consistency, and are prepared to have it tested in this way in
applied scientific ontology.
Combinatorial ontology of the abstract
While applied scientific ontology remains a work in progress, we can
provisionally declare our preference for an abstract subdomain of the
ontology that includes sets and numbers, properties, qualities and
relations, but not propositions. An alternative theoretical applied
ontology could obviously manage these potential metaphysical
properties in a different way, resulting in a different preferred theo-
retical existence domain. Why sets and numbers? Why qualities and
relations? The answer is simply that each can plausibly be regarded as
maximally consistent, in the absence of contrary argument or solid
evidence of their predicational inconsistency or incompleteness.
What about an effort to eliminate properties from the ontology in
something like the manner proposed for propositions, taking up the
explanatory slack in other ways? This, after all, has been the storm
centre of philosophical disagreement about the ontological status of
universals in the hoary dispute between realism or Platonism versus
nominalism. We refer again to the unmet burden of proof to
demonstrate inconsistency or incompleteness generally among
universals on the part of opponents of the existence of abstract
entities. We need not regard logically possible objects and logically
possible properties as real existent entities considered only in
themselves, if we can make a good case against their predicational
consistency or completeness, as with the discovery of a deep concep-
tual paradox in their property combinations, as with the property of
being a barber who shaves all and only those persons who do not
shave themselves. If a sound argument to this effect could be
advanced, it would provide a strong reason for eliminating proper-
ties, qualities and relations as abstract entities from the preferred
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 229
existence domain, leaving others like numbers and sets to occupy
that niche.
The trouble is, without entering into all the necessary details, that
efforts to make particulars only do the work of universals have not suc-
ceeded. To offer only a fleeting sense of the difficulties, consider the
implications of trying to reconstruct the fact that snow is white with-
out admitting white as a universal to the preferred existence domain.
When we argue that the condition of all past, present and future
particular instances of snow are individually considered sufficiently
similar with respect to their effect on normal colour perception as to be
collected together nominalistically under a single term, and that their
common shared whiteness amounts to nothing more than this, we over-
look the fact that, at least in combinatorial ontology, objects do not
stand free and independently of, but are constituted by, their properties.
A special combination of properties constitutes a particular object or at
least serves to distinguish it logically from others. Combinatorially,
properties, even if not existent, are undeniably universal, at least in the
sense that the very same properties go into the constitutive, identifying
and uniquely individuating property combinations of distinct objects,
including the actually existent physical entities encountered in sense
experience. We cannot reasonably appeal to stipulative nominalizations
of similarities observed between multiple objects as a way of doing with-
out universals in the case of abstract particulars like sets and numbers,
if the objects themselves are intensionally defined in terms of particu-
lar property combinations. Applied ontologists like Quine, enamoured
of a desert landscape nominalism, often see all of these issues as more
or less on a par, and strive to eliminate abstract entities of any sort from
the existence domains they prefer. If sets and numbers are reduced to
properties (or propositions) and these are eliminated, then sets and
numbers are also eliminated in one fell swoop.
What about the idea of taking only abstract particular properties as
elements of property combinations? This would be a rough but
presumably not impossible way to proceed. The difficulty is that when
we consider the property combinations [red, ball] and [red, cube], we
seem more naturally to be combining the same abstract universal prop-
erty red with a different second property in each case, thereby provid-
ing distinct intensional identity conditions for these logically possible
objects, and explaining the truth of predications of properties to the
object in unlimitedly many unexemplified states of affairs. If we turn to
abstract particular properties, then we must speak instead of specially
object-indexed property combinations, such as [red
a
, ball
a
] and [red
b
,
cube
b
], where a and b are the red ball and red cube, respectively. We can
230 ONTOLOGY
follow this course if we choose, but then we enter unnecessarily into the
explicit circularity of identifying object a intensionally with [red
a
, ball
a
]
and b with [red
b
, cube
b
]. At this point, we do perhaps finally begin
illegitimately to multiply abstract entities beyond explanatory necessity.
We do so, moreover, at the risk of making all object–property
predications, and hence all states of affairs, logically necessary, since
object a cannot fail to have all and only the a-indexed properties
belonging to its uniquely identifying property combination. For simi-
lar reasons, it will not do to allow abstract entities with few exceptions
to be included only in the actual world. In that case, we cannot begin
with such logical possibilities as the combinatorial analysis of being
requires, including logically possible objects, logically possible proper-
ties and logically possible states of affairs, nor with transworld logical
and mathematical truths, which we seem to require to be available
universally for the constitution of every logically possible world.
It is interesting in this regard that Quine and other formal ontologists
who have tried to eliminate abstract entities have concluded after
strenuous efforts that classes in any case must minimally remain in the
domain in order to make sense of the propositions of mathematics and
science. If classes alone cannot be eliminated from ontology on Quine’s
terms, and if classes are defined as property combinations, then neither
are all properties, universals in the traditional sense, entirely eliminable.
If we use Ockham’s razor only selectively, and abandon the ideal of
wholesale ontological reduction, then we may no longer see it as an
important step forward in applied ontology to commit ourselves with
Quine to classes exclusively as the only abstract entities. We might then
just as well open the floodgates to any putative abstract entities that
prove themselves useful, and against which there is no unanswered
charge of predicational incompleteness or inconsistency.
The unbearable lightness of logically possible being
We have approached the problems of pure philosophical ontology
intensionally, beginning with logically possible properties, and
considering their logically possible combinations with logically possi-
ble objects. Do these terms of the combinatorial theory have any deep
ontic freight of their own? One immediate reaction is to ask, how
could they not? To make an informed answer, we must explore the
consequences of whatever propositions in the pure classical logic on
which we have leaned appear to be ontologically committal.
What, finally, is the ontic status of logical possibilities, on which all
else in a combinatorial theory of ontology logically depends? We say that
ABSTRACT ENTI TI ES, PARTI CUL AR AND UNI VERSAL 231
logic is ontologically committed to logical possibilities and their logical
relations in all logically possible combinations involving all logically
possible objects and all logically possible properties. Are logical possi-
bilities themselves abstract entities, or are they the constituents of all
entities, including abstract ones? If logical possibilities are abstract
objects, then we may be ontologically committed to them by any use of
classical logic, and certainly in combinatorial pure philosophical ontol-
ogy. We have not only not been particularly forthcoming about the ontic
status of purely logical possibilities, but we have argued that, like
Wittgenstein in the Tractatus, we should not try to specify the ontic sta-
tus of logical possibilities in combinatorial pure philosophical ontology.
In the most important sense, in answering the question of being, the
ontic status of logical possibilities does not make any difference.
Is combinatorial ontology committed to a realm of abstract entities?
The answer is yes, if we think that logical possibilities must exist, have
being in a strong sense, in order to constitute the being of the actual
world in any of its parts or moments. We should bear in mind that the
possibilities in question are not all merely logical possibilities, since
exactly one of them must turn out to be the logically contingent actual
world. It would be odd in that case, if not logically incoherent, to regard
the ontic status of logical possibilities as actually existent abstract enti-
ties. The ontological weight of logical possibilities considered only as
such is of negligible importance until their implications are explained
in the combinatorial analysis of being. It is logic that is ontologically
committed to logical possibilities, and only derivatively the combina-
torial analysis of being in so far as it makes use of the presuppositions
of pure classical logic as part of its method. Combinatorial pure
philosophical ontology produces the same answers to the fundamental
problems of ontology no matter what the ontic status of the logical
possibilities the logic combines. The possibilities in question are only
the possibilities of combining elements, where the exact nature and
ontic status of the elements is secondary even when relevant.
Pure classical logic’s ontological commitment to logical possibilities
is at most a light charge. Logical possibilities are equally the constituents
of the actual world and every non-actual merely logically possible
world. They are themselves not existent entities, with the single
interesting exception of the actual world, but only logically possibly
existent entities. Considered as such, even if they are in some sense
universal, logical possibilities are still only logical possibilities. Logic
cannot do without logically possible objects and logically possible prop-
erties in logically possible states-of-affairs combinations. It needs them
in order to be able to formalize the internal logical structure of a
232 ONTOLOGY
sentence as it relates expressively to logically possible inferences in
reasoning. Logic is a formal theory of all logical possibilities, of
predications at the linguistic and symbolic order, and of the possession
of properties by objects in states of affairs in the ontic or metaphysical
order. If we want to do without logical possibilities, even in whatever
form we introduce them into the machinery of combinatorial pure
philosophical ontology, then we will also have to do without logic.
Combinatorial ontology asks only for whatever logical possibilities are
available generally to a logic favoured for the expression and inference
of meaningful sentences, and from these modest materials answers
fundamental questions about the nature of being.
We begin intensionally with properties. Properties are only the
logically possible qualifications of logically possible objects, and the
states of affairs in which a logically possible object possesses a logi-
cally possible property are only logically possible states of affairs.
Logical possibilities, of objects, properties, states of affairs and
worlds, have at the outset only whatever ontic status we eventually
want to extend to logical possibilities generally, knowing that only
one logically possible world consisting of one choice of logically
possible objects and logically possible states of affairs is actual. It is
not asking much for logic to admit logical possibilities, but logic is
nothing without them. Logically possible objects, properties, states of
affairs and worlds are minimally sufficient on a combinatorial analysis
of the concept of being to deduce the necessary existence of the
uniquely existent logically contingent actual world. We start out
intensionally with properties, with meanings, as conceived in pure
logic, and end up with the actual world, with abstract and spatio-
temporal and subjective psychological entities.
The existence of some actual world or other is logically necessi-
tated, although the actual world, its condition and constitution, is
logically contingent in all its physical objects and states of affairs. A
combinatorial theory of being begins with and depends throughout
on the lightest of ontological foundations, the logical possibility of a
logically possible object having a logically possible property. All
logical possibilities are entities on the combinatorial analysis of being
if and only if their constitutive extraontological property combina-
tions are predicationally maximally consistent. If a mere logical poss-
ibility is an abstract entity, it is the ontologically most important of all
abstract entities.
Subjectivity of mind in the
10 world of objective physical facts
Ontology of mind
The occurrence of thought raises difficult issues in applied ontology.
The mind–body problem challenges our understanding of how
thought relates to the established existence subdomains of physical
and abstract entities.
What is a thought and what is the mind? If the mind and its
contents are simply physical entities, if thoughts are simply physical
events in the brain and nervous system of a living organism, then the
ontic status of the mind can be classified without further ado as a
special type of physical entity among others in the universe. The
distinction between internal thought and the external world in that
case is an illusion that collapses entirely into the world of objective
facts about exclusively physical phenomena. If, on the other hand,
thoughts are ineliminable and ontologically irreducible to physical
events, then we must find a way to expand the existence domain to
accommodate the mind and psychological events as something
altogether different from physical and abstract entities.
Physicalism or materialism in the philosophy of mind proposes to
explain mental phenomena reductively as physical occurrences,
primarily in the brain and neurophysiological network. The elimination
or reduction of mental to physical events is sometimes said to be
mediated by environmentally conditioned behaviour or behavioural
dispositions in a variation of physicalism known as behaviourism.
Functionalism is a third type of eliminative or reductive physicalist
theory, according to which psychological events can be discounted in
favour of the mechanical information-processing subroutines
performed by the brain as a living machine, a purely physical entity,
functioning according to abstract rules much like the number-crunching
algorithms of a computer program. We have already established the
234 ONTOLOGY
outlines of an existence domain of physical entities, states of affairs and
events. If thoughts are just neurophysiological events, then no new ontic
categories are required to subsume psychological states. If we can agree
that there is nothing more to mind than a complex physical phenom-
enon considered in neurophysiological, behavioural or functional
terms, then we can solve the mind–body problem in favour of the body.
Whether mental events are reducible to physical events, as many
scientists and philosophers have assumed, is by no means easy to
decide. Although many theorists are encouraged by the impressive
successes of the natural sciences in explaining and predicting other
types of previously mysterious and apparently physically recalcitrant
phenomena, there are good reasons for being sceptical about the
prospects of doing away with or ontologically reducing psychological
events to purely physical events. We must consider the best arguments
reflecting the most important positions on opposing sides in the mind–
body subjectivity–objectivity controversy, and try to sift through the
conclusions that emerge for clues to a correct ontology of mind.
Eliminativism and reductivism
A significant ontological economy is achieved by eliminativism and
reductivism in the philosophy of mind. Eliminativists argue that there
really is no such thing as mind, that there are at best misleading
appearances of consciousness and mental content. Reductivists
similarly hold that while psychological phenomena are real, they do
not belong to a special ontic category of their own, but can be satisfac-
torily explained by reference to exclusively physical phenomena and
their abstract properties.
There are as many forms of eliminativism as of reductivism. Both
“isms” begin with scientific findings about the brain and nervous
system and externally verifiable facts about the behaviour, including
verbal behaviour, of a psychological subject. Thus, they stand in stark
opposition to any form of phenomenology that does not allow itself
to be fully explained and its conclusions fully recovered only from an
external impersonal or third-person standpoint. We have already
mentioned materialism, behaviourism, and functionalism as physical-
ist theories of mind, to which we now add the qualification that there
can be either eliminativist or reductivist versions of these three types
of theory. It should be clear that if any of these six versions of
physicalist theories is true, then there is no need at all to tack on
another category to the preferred existence domain as we have
characterized it up to this point, or even to establish a separate
SUBJ ECTI VI TY OF MI ND 235
subcategory of psychical entities for psychological phenomena. If
thought does not really exist, or if we can manage to say whatever can
legitimately be said about the mind in an explanatory reduction in
which no mental or psychological concepts occur, then there is no
need to expand the ontology of physical and abstract entities that we
already have in place in order to take adequate account of the nature
of thought.
1
In their rejection of first-person subjectivity as unscientific, both
eliminativism and reductivism are opposed to any theory of mind that
maintains a difference between the externally verifiable properties of
the psychological subject, and any supposedly internal aspect of mind.
They are particularly interested in disputing what common sense and
phenomenology refer to as the qualia and intentionality of thought.
These are the properties of lived-through psychological content, or
what it is like to experience a certain thought or type of thought, and
the “aboutness” or direction of a thought towards an object, by which
a thought refers to, intends or is about this or that existent entity or
nonexistent object.
2
By rejecting the qualia and intentionality of thought as real proper-
ties or as ontologically distinct from physical or abstract properties,
eliminativism and reductivism propose more or less radically to
streamline the preferred existence domain to what we have thus far
characterized as the applied scientific ontology of existent physical
and abstract entities. The question of whether such an elimination or
reduction of psychological phenomena can be accomplished by
materialism, behaviourism, functionalism or any other imaginable
theory of mind has become the major bone of contention among
disputing philosophical factions in their efforts to address the mind–
body problem. The undecided ontic status of thought, consciousness
and the mind thus boils down in theoretical terms to the undecided
ontic status of qualia and intentionality.
Although eliminativists are still very much a force in contemporary
philosophical psychology, their efforts to deny the obvious first-person
facts of consciousness need not be taken as definitive. Some philos-
ophers have claimed that eliminativism is so blatantly false and coun-
ter-intuitive that it can be discounted without further argument. They
defy the eliminativist to deny the existence of a howling toothache or
the sensation of colour in a field of flowers.
3
This complaint might be
justified, but it does not go to the heart of the eliminativist stance, which
attempts to acknowledge these reported counter-examples as false
appearances. A more powerful objection to eliminativism is that the
approach is logically incoherent, for in acknowledging that there are
236 ONTOLOGY
appearances, true or false, of first-person conscious thoughts exhibit-
ing qualia and intentionality, eliminativists thereby admit the existence
of consciousness. What is an appearance, after all, but a psychological
occurrence, a thought or experience, in which there is veridical or
illusory mental content that in this case is reflexively about the occur-
rence itself, whether or not an eliminativist wants to say that it actually
exists? If even the appearance of thinking is not itself already a thought,
then what is it exactly that eliminativists are supposed to be denying?
If eliminativism is as confused as it appears, we can best proceed
by setting aside its implausible refusal to acknowledge the existence
of thoughts, and concentrate more profitably on reductivist pro-
grammes in behaviourism, materialism and functionalism. We must
inquire whether any of these reductivisms satisfactorily answer the
mind–body problem, or whether the qualia and intentionality of
thought are ultimately explanatorily irreducible, justifying an addi-
tion to the preferred existence domain, alongside physical and
abstract entities. If so, then we must institute a special new category
for ontologically irreducible thoughts, psychological phenomena and
states of affairs that is not just a combination of purely physical and
purely abstract entities. As the arguments are considered, we discover
good reasons for renouncing any form of reductivism, in support of
the contrary thesis that qualia and intentionality are explanatorily
irreducible. We thereby arrive at an appreciation of the ontologically
irreducible subjectivity of mind in the world of objective facts.
Materialism, behaviourism, functionalism
The advantage of any type of reductivism by comparison with
eliminativism in the philosophy of mind is supposed to be that it avoids
the embarrassment of denying the existence of thought. Anyone can
and everyone does experience introspectively psychological states at
first hand. At the same time, reductivism allows explanations of
psychological phenomena to be given in third-person scientifically
respectable causal terms involving publicly verifiable properties of
purely physical entities and events and their purely physical and
abstract properties. We examine three main types of reductivism, and
conclude that none justifies the explanatory or ontological reduction
of psychological phenomena to purely physical entities.
Materialism tries to reduce psychological events to facts about a
subject’s neurophysiological states. These are usually understood to
include antecedent conditions and the impact of environment in a gen-
eral framework of causal connection among physical events governed
SUBJ ECTI VI TY OF MI ND 237
by natural scientific law. Materialism in that sense is the most basic form
of physicalism. It holds that whatever we might otherwise want to say
about the qualia and intentionality of internal psychological states can
be explained in terms of the external material properties of the brain
and nervous system of a psychological subject. A thought is then
identical with, nothing other than or over and above, a material neuro-
physiological occurrence. It is an electrochemical transaction within the
complexly connected neural connections in a certain living material
entity, the brain and its nervous systems. Thought in principle can then
be understood in terms of its material constituents and their physical
properties interrelated in a complicated biological system, causally
interacting with each other and less immediately with the substances
and events of the external material world.
4
Behaviourism has several forms, but is generally the theory that all
psychological phenomena are reducible to occurrent behaviour or
conditional counterfactual behavioural dispositions. A classic example
is one in which behaviourism, despite, or perhaps because of, its over-
simplification, eliminates or reduces references to pain as a mental
episode in preference to pain expression, such as moaning, wincing,
crying, tending an injured body part, seeking aspirin or the like. A
dispositional behaviourism, also sometimes known as logical, analytic
or philosophical behaviourism, does not require that psychological
phenomena be explanatorily and ontologically reduced to concurrent
expressions of behaviour, but to the tendency to engage in such behav-
iours when certain conditions are satisfied. I might have such strong
control over my behaviour even when I am in pain that I do not
immediately groan out loud. The dispositional behaviourist will argue
that I am nevertheless disposed to do so, or probably would do so, if I
were by myself or under the relevant disinhibitory circumstances.
5
Functionalism is similar in some ways to behaviourism. It empha-
sizes the correlation of inputs and outputs of information to and from
a computer. The mind is an information-processing machine, accord-
ing to functionalism, one specific formulation of which has come to
be known as computationalism. A functionalist account of psycho-
logical processes can be articulated in an information flow and
control diagram. The diagram features decision boxes and action
modules and arrows indicating how the components of the informa-
tion-processing device are supposed to relate and interact, along with
the direction of information processing, as in the formal description
of a computer program. The analogy between computer hardware
and software is often exploited by functionalism as part of its solution
to the mind–body problem. The body is described as the hardware
238 ONTOLOGY
and the mind as its operating software program, processing informa-
tion in a rule-governed way in real time. The hardware and software,
the neurophysiology of a psychological subject and the information-
processing program by which input is converted to multiple
modalities of output, requires an intimate connection and exact inter-
action of neurophysiological information-processing structures.
According to functionalism, neither body nor mind can be adequately
understood as a separately existing, separately functioning entity.
Mind and body must rather be considered as an integrated well-oiled
machine that some functionalist philosophers and cognitive scientists
prefer to speak of as mind–body.
The standard objections to materialism and behaviourism have
emphasized the advantages of functionalism over its rivals as a reduct-
ivist theory of mind. Materialism is criticized for its limitation to
specific kinds of material entities and events in explaining the nature
of thought. We do not know that the only kinds of material substances
that can support psychological phenomena are those that happen to
be found in terrestrial life forms, in the physical stuff that makes up
the thinking things in the particular part of the universe that we
inhabit. If, on the other hand, we establish an open-ended list of
material substances capable of sustaining thought, then we never
arrive at a philosophically satisfactory explanation of the concept of
mind, because a list of instances is never a substitute for conceptual
analysis. Behaviourism in any of its guises, concurrent or disposi-
tional, in stimulus-response (S-R) or operant conditioning models, is
faulted for being too crude to account for the full range of complex
psychological occurrences it is meant to explain. An example of the
difficulties behaviourism encounters concerns a subject who must be
judged behaviourally as thinking about Bach rather than Brubeck or
Brubeck rather than Bach. The subject’s psychological state arguably
cannot be exactly behaviouristically determined, regardless of
whatever manifest behaviour or dispositions to behave are evinced, if
the subject is honestly mistaken about the conventions for communi-
cating the content of the thought, and intends to express Brubeck by
the name “Bach”, pointing to pictures of Bach, recordings of Bach’s
music, and the like, and intends to express Bach by such conventions
as uttering or being disposed to utter the name “Brubeck”, while
indicating pictures and recordings of Brubeck.
Functionalism is thought to enjoy a special advantage over materi-
alism. It is deliberately not limited to any particular material
substance, such as the largely carbon-based cytoplasm of human
neurophysiology as life happens to have evolved on our planet.
SUBJ ECTI VI TY OF MI ND 239
Functionalism can explain psychological states, events and occur-
rences involving any type of material substances, provided only that
they are functionally properly so organized and interrelated as to
support equivalent information-processing functions, converting
information input to output in identical ways with different types of
hardware. Accordingly, once again, we narrow our focus, this time to
functionalism, as the most promising, currently popular version of
explanatorily and ontologically reductivist philosophy of mind.
Functionalism has philosophically interesting implications that
some theorists believe provide additional justification, but that critics
of the theory have declared an outrageous reductio ad absurdum, of the
theory’s basic principles. It is supposed to follow, for example, that a
sufficiently large number of persons holding cards reading “0” or “1”,
like the machine language of a digital computer, orchestrated in their
movements relative to one another so as to exactly simulate an appro-
priate information-processing program, would not only formally
model the mind’s information-processing protocols, but would
replicate thought by instantiating self-consciousness. The danse maca-
bre of 0’s and 1’s is supposed to constitute a living intelligence, indis-
tinguishable, since the exact medium of information processing is
irrelevant to functionalism, from the natural biological mind whose
software program is thereby duplicated.
6
Philosophical opinion varies diametrically as to whether such results
are interesting implications or self-refuting absurdities. Contemporary
philosophical psychology is sharply divided over just such issues as these
about the existence and nature of the mind. A further, even more
intriguing and correspondingly more controversial implication of func-
tionalism is its philosophical underpinning for artificial intelligence,
which seeks mechanically to reproduce real psychological occurrences
by programming a digital computer with the mind’s software of infor-
mation-processing algorithms. If the exact hardware by means of which
strings of 0’s and 1’s are input to a processor and transformed by the
appropriate software into output in a rule-governed way is irrelevant
to the explanation of psychological phenomena, then it should be
possible in principle to construct a mechanical mind out of any suffi-
ciently complex digital computing machinery. Artificial intelligence
thereby at once becomes a computer laboratory in which the function-
alist thesis can be tested, and a prospective goal and vindication for
functionalism — if, that is, functionalism’s or computationalism’s
implications for the possibility of what is sometimes described as strong
or mentalistic artificial intelligence should turn out to be feasible, and
the opposite if they are not realizable.
240 ONTOLOGY
The main difficulty with functionalism as an adequate reductive
theory of mind is approximately the same as that of behaviourism.
The analogy between behaviourism and functionalism is straight-
forward if we think of the inputs and outputs that are supposed to be
processed algorithmically by the mind or by any material device
capable of transforming information by the equivalent of a computer
program on the functionalist thesis. We see that these are not so
different from the correlation of input environmental stimuli or
scheduled operant conditioning and output behaviour or dispositions
to behave described by alternative versions of behaviourism. Some
behaviourists even speak of the individual psychological subject as a
kind of black box, the exact biological and neurophysiological opera-
tions of which a behavioural science neither needs to nor can intelligi-
bly investigate. This is just how functions generally are defined,
whether in mathematics or functionalist psychology or philosophy of
mind. The arithmetical function of addition is just such a black box.
There are numerous possible algorithms but no definite answer to the
question of how addition converts 2 and 3 into 5. Addition in this
elementary calculation really is nothing more than the correlation,
among endlessly many other combinations, of the inputs 2 and 3 with
the output 5. The problem with functionalism, as with behaviourism,
is that we do not have an adequately sensitive way, merely by correlat-
ing inputs and outputs of information, in effect, coded strings of 0’s
and 1’s, of distinguishing reductively between a subject’s thinking
about Bach or Brubeck, based purely on what goes into and what
comes out of the information-processing black box.
If functionalism is the best hope for a reductive philosophy of mind
that has no need to refer to the ostensible internality and privacy of
thought, that avoids speaking of qualia or intentionality, then the
prospects for a theory whose applied scientific ontology consists only
of physical and abstract entities with no special third category for
mental or psychological entities do not seem particularly promising.
We now consider two alternatives to mind–body reductivism that
have appealed to non-reductivists in the study of mind, known as
substance and property dualisms.
Cartesian substance dualism
A non-reductive philosophy of mind requires significant adjustment in
the preferred existence domain, an addition to its previously estab-
lished categories of physical and abstract entities. It is found in a still
more traditional philosophy of mind, often referred to as substance or
SUBJ ECTI VI TY OF MI ND 241
Cartesian dualism, named after Descartes, the philosopher with whom
this way of understanding the mind is most frequently associated.
According to substance dualism, there are two different kinds of
substance – physical and mental or spiritual substance, bodies and
minds – that are ontologically distinct but integrated in a living
psychological subject. There are several versions of Cartesian dual-
ism, not all of which were explicitly defended by Descartes. Some
variations of substance dualism in particular are designed to enable
Descartes’s distinction between mental and physical substances to
meet a variety of philosophical objections. What they have in
common is an ontological commitment to the body and mind as
separate but interrelated entities. Beyond their shared distinction
between the body and mind or soul, substance dualisms disagree in
particular on whether or not physical and spiritual substances can
causally interact, as Descartes believes, or whether they are related at
most only more abstractly. God, also, in Descartes’s system, as in that
of most other mind–body substance dualists, in contrast, is a purely
spiritual entity, and, in Descartes’s metaphysics, a pure mind of infi-
nite substance. In some versions of substance dualism, God sustains a
divine pre-established harmony between mental and physical events,
keeping both synchronically correlated together in parallel tracks.
Substance mind–body dualists, unlike eliminative or reductive
materialists, behaviourists or functionalists, add something categori-
cally new and different to the basic ontology of physical and abstract
entities. The mind or spirit or soul as a distinct kind of spiritual
substance cannot be assimilated in or subsumed under either the
physical or abstract realms of a preferred existence domain, but
requires its own unique subdomain. Descartes, nevertheless, sees an
important gain for religion in his metaphysics of substance dualism,
since he believes it implies that the mind, spirit or soul need not perish
with the physical body, but might and even must survive its death in a
continuing spiritual existence. This is a traditional idea of the soul
integral to Descartes’s Catholic Christian religious background, that
is also taught by many other world religions. The previously described
categories of ontology must be expanded if a substance dualist
philosophy of mind is accepted, to accommodate physical, mental or
spiritual and abstract entities. The minds of psychological subjects, as
distinct from their bodies, especially from their brains and nervous
systems belonging to the ontology of physical entities, must then be
classified as mental or spiritual entities, in a category that might also
be adapted to include God as a supreme mind or divine spiritual
being.
242 ONTOLOGY
Substance dualism, despite its implications for the contra-causal
freedom of will and the immortality of the soul, has had few
adherents in contemporary philosophy of mind, and as a result has
had little impact on the choice of a preferred existence domain for the
ontology of mind. Objections to substance dualism include the argu-
ment that appeals to mental entities as a separate applied ontological
category are not needed in order to explain psychological phenomena
scientifically for thinkers attracted to some form of eliminative or
reductive philosophy of mind, and thus go by the board thanks to
Ockham’s razor. Another complaint urges the difficulty of accounting
for mind–body causal interaction on the substance dualist thesis. We
want to be able to do justice to the fact that mental events like
decisions, beliefs and desires can cause the body to do certain things,
and that physical occurrences of many kinds can in turn bring about
specific types of mental events. All perception of the external world
needs to be explained in something like this way in a substance dualist
framework, as would such mental events as pain experiences occa-
sioned by damage to nerve endings, altered states of consciousness
induced by drugs, and many others besides.
By consigning minds to a distinct ontological category different
from physical entities, substance dualists like Descartes require the
mind and its thoughts to be non-spatiotemporal. The presumption
that thoughts while occurring at specific times or during specific
intervals of time have no particular spatial location is sometimes con-
sidered as good evidence in support of mind–body dualism against
any form of eliminativism or reductivism in the philosophy of mind.
Such a classification, unfortunately, as critics of the theory are quick
to point out, seems metaphysically incompatible with the possibility
that the body and mind might causally interact. It implies that while
the body and all its parts have definite spatial locations, the mind as a
spiritual substance is literally nowhere. Where, in that case, can the
body and mind causally interact? Where can they touch one another
in space and time to bring about a change of state by transfer of en-
ergy, as we expect from our knowledge of all other types of causal
interaction? If there is no answer, and no plausible way of discounting
the question, then the prospects of substance dualism may be
unpromising in the extreme, as critics hostile to the theory on these
grounds have concluded.
7
A related objection in modern physics is
that while Cartesian dualism entails that the mind as a spiritual sub-
stance with its thoughts is non-spatial, as intuitively it sometimes
seems to be, thought is nevertheless supposed to be temporal.
Descartes and most other theorists, whether or not they are substance
SUBJ ECTI VI TY OF MI ND 243
dualists, provided only that they are not eliminativists, believe that
thinking occurs in real time, which is impossible if space and time are
not scientifically distinguishable dimensions, but united in a single
relativistic spacetime continuum. If substance dualism is unacceptable
on its own terms for any of these reasons, then spiritual substance,
distinct from physical and abstract entities, should not be added to a
preferred existence domain.
Virtues of property ÷ ÷÷ ÷÷ substance dualism
There is another type of mind–body dualism that is different from
Cartesian substance dualism, and that deserves serious mention in the
context of exploring an alternative ontology of mind. This is the
theory of property or aspect dualism. Property dualism is not a
concept of mind that requires a separate ontological subcategory of
mental or spiritual substances, but one that in some formulations
necessitates a different kind of revision of the received ontology of
physical and abstract entities.
Property dualism does not hold that the mind transcends the body.
We have already indicated that there is no room in a combinatorial
ontology for transcendent entities. Whereas some philosophers,
notably Kant, the later Husserl and the early Wittgenstein, argued
that the ego or “noumenal” or “metaphysical” self or “philosophical
I” is in some sense transcendent, we have seen that the concept of
mind, self, soul or ego transcending the actual world at large is
logically incompatible with the combinatorial analysis of being as
maximal consistency. If these conclusions are correct, then transcen-
dental mental entities are necessarily excluded from a preferred
existence domain in an applied scientific ontology of mind. Property
dualism is different from eliminative and reductive philosophy of
mind, the metaphysics of substance dualism, and the theory of the
mind’s transcendence.
8
There are interesting similarities between property dualism and the
theory of the transcendence of mind. The first and most obvious
parallelism is that both approaches deny mind–body reductivism and
affirm the reality of thought and mental content, in defiance of
eliminativism. Property dualism, like substance dualism, rejects the
model of mind whereby mental states are identical with physical
states. There are various forms of property dualism. The most tenable
is perhaps a version of the theory whereby thought is both physical –
has a physical neurophysiological aspect – and also a mental non-
physical aspect, by virtue of exemplifying qualia and intentional
244 ONTOLOGY
properties that cannot be reduced to or adequately explained in terms
of physical qualities and relations. If qualia and intentionality cannot
be satisfactorily reduced as proposed by materialism, behaviourism or
functionalism, then there are properties of mind that are not purely
physical.
We focus for the moment on the intentionality of thought, and
return later to the relation between qualia and intentionality. Inten-
tionality or aboutness on some accounts is a primitive irreducible
abstract relation holding between thought and its objects. There are
good but not unchallenged reasons for thinking that intentionality
cannot be explained reductively in terms of non-intentional concepts.
One argument is that thought appears phenomenologically to be
capable of intending nonexistent objects, and that the intentionality
of decision-making in action is directed toward nonexistent as yet
unrealized or unactualized states of affairs. A contemplated action is
intended to achieve its intended object only thereafter in trying to
bring it about as an actual state of affairs, and may or may not succeed
in actually doing so. A reductive account of mind must explain or
explain away the intentionality of thought in terms of physical prop-
erties causally interrelated like other physical occurrences. If inten-
tionality sometimes involves a relation to nonexistent objects, like my
as yet merely dreamed-of visit to Sifnos, then such thoughts cannot be
adequately explained physically or causally. The reason is that in such
explanations only actual physical entities and events involved in
actual real-time causal interactions can be mentioned. Here there may
also be a clue to understanding the freedom of thought, will and
action, all interlinked because of the intentionality of mind, and
frequently understood to be an essential presupposition of moral
responsibility and moral value.
The intentionality of thought, if it cannot be explained in a physi-
cally reductive way or explained away as an illusion and philosophical
confusion, superadds a non-physical dimension, a second side or
hidden facet concealed from the hard psychological sciences, to the
physical neurophysiological properties of mind. The ontology of
mind must then make provision for non-physical aspects of thought,
and in particular for intentional states that may be different in onto-
logical kind from purely neurophysiological states. Property dualism
so conceived does not add any ontologically new entities, if we are
literally just counting heads. It does not add any unprecedented non-
physical substances to the physical and abstract entities we have
already granted or concerning which we may remain sceptical. The
theory nevertheless introduces a category of properties that involve
SUBJ ECTI VI TY OF MI ND 245
the abstract relation of intentionality as a property of appropriately
neurophysiologically complex physical entities such as ourselves and
notably involving our brains and nervous systems.
The mind, according to property dualism, has two different aspects
by virtue of its distinct types of properties. It has physical and non-physi-
cal properties, the latter category including qualia and the intentionality
of thoughts. The mind has an external side which it shows to the
cognitive sciences, and an internal first-person side, which is known
only introspectively by the first-person subject in first-person experi-
ence. Substance dualism is not implied; only the neurophysiology of a
psychological subject in a qualia-bearing intentional state. If we deny
this dual aspect of thought, its cognitive scientific third-person outside
and its phenomenological first-person inside, or if we fail to look for the
right kinds of answers to the right kinds of questions in the appropri-
ate side of the first-person–third-person division of a cognitive subject
in a more broadly scientific investigation of the mind, then we are
certain to misunderstand the nature of consciousness, to oversimplify
psychological faculties, and deny what is obvious to reflection about the
content and reference of conscious thought.
Such criticisms are directed only at third-person eliminativism and
reductivism as philosophical ideologies, and not against the important
scientific discoveries made by cognitive science. When cognitive science
fills in another missing piece of the puzzle about how the mind processes
information and controls motor activities, we may have significantly
increased our knowledge about the mechanics of thought. Why
suppose, however, that what even the best third-person science delivers
about the workings of the mind gives us a complete picture? Why do so,
especially when we have good even if defeasible reasons to believe from
the only acceptable source, our own individual first-person introspec-
tive or phenomenological experiences, that the mind must be a dual-
sided kind of thing, with an outside that others can examine and an
inside that only we as first-person subjects can non-inferentially know?
We can freely accept non-reductive materialism, non-reductive
behaviourism and non-reductive functionalism in a property dualist
philosophy of mind. All such theories make important contributions to
our understanding of the concept of mind in its physical aspect. They
do not by themselves solve the mind–body problem, if the objections we
have raised are correct. Nor as a result do these non-reductive theories
determine the ontology of mind. If the mind also has physically irreduc-
ible aspects involving the qualia and intentionality of thought, as we
have argued, then the preferred existence domain for a correct applied
ontology of mind must include a special subcategory of irreducibly
246 ONTOLOGY
subjective psychological phenomena alongside the previously estab-
lished subdomains of purely physical and abstract entities. The mind in
that case is not purely physical or abstract, but something different, by
virtue of its physically irreducible qualia and intentionality.
Property dualism interposes a third applied scientific ontological
subcategory in the preferred theoretical existence domain, in much
the same way that substance dualism, if accepted, would introduce a
new subcategory of spiritual entities. The character of the addition to
the applied ontology of mind is obviously very different in the case of
property dualism than for substance dualism. The mind, according to
property dualism, is not altogether a non-physical entity. It has all the
physical properties of its neurophysiology, behaviour and informa-
tion processing that are investigated by the hard psychological and
cognitive sciences, together with the non-physical properties that
disqualify it as a purely physical entity. Consciousness for property
dualism is an episodic succession of qualia-bearing intentional states
lived through by a thinking subject in real time. This makes it appro-
priate to allow phenomenology as well as neurophysiology and
behavioural science in the study of mind. We have not objected to
phenomenology in philosophy generally, but only to its application in
what purports to be pure philosophical ontology, as in Heidegger’s
metaphysics. Ockham’s razor does not legislate against introducing
property-dualistic minds into the applied ontology unless the ex-
planatory needs in philosophical psychology for which qualia and the
intentionality of thought are emphasized can be satisfied in another
way in terms of purely physical and abstract entities alone, levelling
the three proposed applied ontological subcategories back to two. It is
unclear that there are any immediate prospects for successfully effect-
ing this kind of ontological reduction.
Supervenience in the ontology of qualia and intentionality
The intentionality of mind, as we have urged, is complemented by its
qualia or lived-through qualitative content of thought. A quale, in the
singular, is what it is like from a thinker’s first-person perspective to
experience a certain type of thought. Seeing a colour or tasting a
claret or feeling grief or lust or joy or the satisfaction that comes from
understanding a difficult mathematical proof are sufficiently sugges-
tive examples. The relation between qualia and intentionality is a
difficult problem for property dualism.
Qualia and intentionality phenomenologically go together, but
thought content evidently underdetermines a thought’s intended
SUBJ ECTI VI TY OF MI ND 247
object. There is no reason why the Taj Mahal could not be intended
by a thought whose qualia or content is the equivalent of a mental
image of the Statue of Liberty or the Blue Mosque of Istanbul. Like
the intentionality of thought, qualia have proven to be resistant to
efforts at theoretical elimination or reduction to purely physical
non-intentional entities, and equally essential to a complete under-
standing of the nature of thought and the concept of mind. The
stubborn recalcitrance of qualia and intentionality to reductive
strategies in philosophical psychology has motivated some philos-
ophers to deny or ignore these properties of mind in order to clear
the way for a more traditionally scientific account of psychological
phenomena. We cannot satisfactorily solve genuine philosophical
problems, however, simply by denying the evidence from which the
problems arise.
If it is true that thought possesses both qualia and intentionality,
how, if at all, are they related? There is an interesting argument to
suggest that qualia and intentionality must be logically independent
of one another. Hilary Putnam’s Twin Earth thought experiment
implies that two or more thinkers, neurophysiologically indistin-
guishable in every way, can have identical qualia, despite intending
different objects on Earth and Twin Earth. Twin Earth is exactly like
Earth, except that on Earth water is H
2
O, whereas on Twin Earth
water is XYZ. Putnam assumes that thinkers on Twin Earth are
molecule-for-molecule identical with thinkers on Earth, discounting
the water in their bodies, apparently, so that everyone on Earth has
a Twin Earth doppelgänger. Putnam assumes that mental states
supervene on physical states, so that the qualia or thought contents
of Earth thinkers and their Twin Earth doppelgängers are identical.
If my Twin Earth counterpart and I both think “Water!”, then the
experience or thought contents of our desires for or beliefs about
water are qualitatively identical. If Earth water is H
2
O and Twin
Earth water is XYZ, then my doppelgänger and I nevertheless
referentially intend different objects when we both desire or believe
that there is water. The implication is that qualia and intentionality
must be different, logically independent from and unrelated to one
another, because a thinker on Earth and the thinker’s Twin Earth
doppelgänger can have identical qualia even when their thoughts
intend different objects.
9
Despite such arguments, there is a sense in which qualia and inten-
tionality are interdependent. Wherever an intentional state occurs, it
is accompanied by qualia, and conversely. Qualia, indeed, can be
classified as at once the phenomenologically indistinguishable contents
248 ONTOLOGY
and intended objects of certain reflexively intentional psychological
states. Conceivably, then, qualia and intentionality need not always if
ever be two different things, but rather the same thing considered
under two phenomenologically related descriptions, or perhaps as two
logically interimplicative properties of a unified mental state. Alterna-
tively, qualia and intentionality might be understood as two distinct
aspects of thought, related in such a way that one never occurs with-
out the other. Intentionality, introspection teaches, requires no specific
content to determine reference to a particular intended object. If inten-
tionality, as some theorists have argued, is a conceptually primitive
logically irreducible abstract relation between thought and its object,
then an act of thought intends or is about an object directly without
mediation by qualia.
We can think of the connections between neurophysiological
physical states and the qualia and intentionality of a thought in terms
of a supervenience relation. Supervenience is a concept frequently
adduced in philosophical psychology to explain how thought is
produced by and emerges from its neurophysiological foundations.
There are several different theories of supervenience, defining the
concept in different ways. Some of these are so weak as to apply to
part–whole or mereological relations, in such a way that a whole
entity is said to supervene on the sum of its parts.
10
This is a useful
model of supervenience for many purposes, but we are looking for
something stronger as an adjunct to property dualism. We seek a
theory of supervenience according to which the entity that supervenes
on its supervenience base is not only different from its base, but has
properties that cannot be explained in terms of the properties of its
supervenience base.
11
Such an account of supervenience is also some-
times known as a theory of ontological or metaphysical emergence.
12
We can informally define supervenience somewhat more precisely in
terms of the four conditions indicated below.
An important consequence of conditions (iii) and (iv) is that the
analysis establishes an asymmetry or one-way dependence relation by
which, if a supervenes on supervenience base b, then b cannot in turn
supervene on a. This is what we should expect of the concept of
supervenience if it is supposed to reflect the idea that where a super-
venes on b, a is emergent from b in the sense that a has properties that
cannot be satisfactorily explained in terms of the properties of b.
We shall now describe the connections between a psychological
subject’s underlying neurophysiology, qualia and intentionality, as
involving this sort of one-way dependence type of supervenience in
a supervenience hierarchy. Qualia supervene on intentional states,
SUBJ ECTI VI TY OF MI ND 249
which in turn supervene on neurophysiological states, but not
conversely, in either case or at either level of supervenience. The
transitivity of supervenience, guaranteed by the transitivity of
sufficiency relations in condition (ii) (where, intuitively, if a is suffi-
cient for b, and b is sufficient for c, then a is sufficient for c), entails
that qualia, by virtue of supervening on intentional states, also
supervene on a subject’s neurophysiology as the ultimate super-
venience base. The relations between qualia, intentional states, and
the underlying neurophysiology are depicted in the following
configuration, reading the arrow “÷” as the asymmetric ontic and
explanatory dependence of supervenience, and structured in such a
way that: neurophysiological states ÷ intentional states ÷ qualia.
The one-way ontic dependence of supervenience further entails
that all properties of a supervenient entity cannot be adequately
explained in terms of the intrinsic properties of its supervenience
base. The important element is the converse relation that holds
between sufficient conditions and the requirements of adequate
explainability. If the possession of property G is sufficient for
something’s also possessing property F, but not conversely, then F or
the possession of property F by an object can be explained by its
possession of property G, but not conversely. If property G is
sufficient for property F, then there is no property of G that cannot
be understood in terms of property F. In that case, F either already
contains all of G, perhaps in addition to other properties, or is
Analysis of supervenience (ontological or metaphysical
emergence)
An entity, property or state of affairs a, supervenes on an entity,
property or state of affairs b, just in case (logically or nomically,
etc.) necessarily, for every object x and every property F in a:
(i) if x has F, then there is a property G in b such that x has G;
(ii) if any object y has property G, then it also has property F
(thus, having property G is sufficient for something to have
property F);
(iii) it is not necessarily the case that if any object y has property
F, then it also has property G (having property F is not
sufficient for having property G);
(iv) a intrinsically possesses at least one property H that is not
intrinsically a property of b.
250 ONTOLOGY
anyway such that whatever has property F also has property G. In
explaining F, under these circumstances, therefore, one automati-
cally also explains the property G. The reverse, however, is not true,
where the supervenience relation is instantiated, if the possession by
an entity of property F is not sufficient for the possession of
property G.
If intentional states supervene on neurophysiological states, then
intentional states likewise have properties that cannot adequately be
explained in terms of the properties of the neurophysiological states
on which intentional states supervene. If qualia supervene directly on
intentional states, and hence, by virtue of the transitivity of superveni-
ence, indirectly on neurophysiological states, then qualia will also
have properties that cannot be adequately explained in terms of the
properties of the intentional or neurophysiological states on which
qualia directly, in the case of intentional states, or indirectly, in the
case of neurophysiological states, supervene. This is what we should
expect, again as an implication of the distinction between knowledge
by description in the case of intended reference, and knowledge by
acquaintance in the first-person experience of qualia. In both cases,
the opposite will not be true. By virtue of the neurophysiological
states in question being a sufficient supervenience base for qualia and
intentional states, the neurophysiological states in question cannot
possess any properties that the supervenient qualia and intentional
states to which they give rise do not also possess. The concept of
supervenience provides that there is always at least one intrinsic prop-
erty of the supervenient entity that is not an intrinsic property of its
supervenience base, considered only as such. The intrinsic intention-
ality of intentional states is not shared by the neurophysiological base
on which they supervene. The intrinsic lived-through content or raw
feeling of qualia in turn is not shared as an intrinsic property of the
intentional states or neurophysiological base on which they super-
vene, again considered only as such.
The ontic dependence of supervenient intentionality on a neuro-
physiological base has interesting implications. It helps to explain the
fact that we cannot give a phenomenologically or folk psychologically
adequate account of intentional states purely in terms of neuro-
physiological states, whereas we can in principle give a perfectly
satisfactory hard scientific psychological explanation of neurophysi-
ological states without invoking the intentionality of experience or the
thought contents of qualia. It is the same in the case of qualia relative
to their supervenience base in intentional states and ultimately in
neurophysiological states. Qualia are themselves the phenomeno-
SUBJ ECTI VI TY OF MI ND 251
logically indistinguishable objects and lived-through contents of reflex-
ively intentional states. We cannot, accordingly, adequately explain
qualia generally without explaining them as the objects of reflexively
intentional states. Nor can we adequately explain qualia merely as
reflexively intentional states, because they have at least one additional
property or belong to at least one natural kind that is not shared by
intentional states considered only as such; namely, the way they
subjectively feel or what it is like for the first-person subject when they
are experienced.
It is by virtue of the transitivity of supervenience that qualia super-
vening on intentional states can be said indirectly to supervene on the
neurophysiological foundation of intentional states. The application
of the model to the metaphysics of neurophysiology, intentional states
and qualia requires that qualia, like intentional states, supervene
ultimately on a psychological subject’s neurophysiology. The model
also accommodates two major presumed phenomenological or folk
psychological data about qualia and intentionality that might be
offered as data and criteria of adequacy for any satisfactory theory of
the interrelation between qualia and intentionality. We can thereby
explain the impression that intentional states and qualia are always
found together, without supposing that any particular qualia are
definitive indications of any particular intentional state. We can also
explain the presumed fact that qualia are themselves also the intended
objects of reflexively intentional states, in which the content of
experience and its intended object coincide in episodes of reflective
self-consciousness.
If qualia can be explained in terms of intentionality, but not
conversely, then qualia, despite always being accompanied by some
intentional state or other, supervene on intentionality, and not the
other way around. If qualia supervene on intentional states, then
intentionality is also explanatorily more fundamental than qualia.
The hard psychological scientific facts of neurophysiology, or what-
ever supervenience base an experience happens to have, for the same
reason, are also, as we should probably expect, explanatorily more
fundamental than any folk psychological facts about qualia or inten-
tionality. The quarrel between folk psychology and eliminative or
reductive philosophy of mind, whether in the form of materialism,
behaviourism or functionalism, is a dispute about whether adequate
explanations of psychological phenomena need to go beyond their
neurophysiological supervenience base. The ground-level explana-
tion of the least controversial facts of human psychology on the
supervenience model is human neurophysiology and its physical and
252 ONTOLOGY
information-processing substrate. If a certain neurophysiology is
duplicated, according to the concept of supervenience, then a certain
intentional state and certain qualia are also duplicated. But not
conversely. Particular supervenient qualia, as we also know from the
Twin Earth problem and related thought experiments, do not reliably
indicate any particular associated intentional state, or any particular
underlying neurophysiological state.
We can obtain the same intentional state from an unpredetermined
number of different neurophysiological states. The transitivity of
supervenience further implies that in principle we can obtain the same
qualia from an unpredetermined variety of neurophysiological states,
and hence from an unpredetermined variety of intentional states. An
intentional state, supervening on a neurophysiological state, as a
result, is also in part or in one of its aspects a neurophysiological state.
But not conversely. A quale, supervening on an intentional state and
ultimately on a neurophysiological state, as a further result, is both an
intentional state and a neurophysiological state. Again, however, not
conversely. It is possible for intentional states to intend, among
indefinitely many other things, their own neurophysiological super-
venience base or supervenient qualia, or both, as when a thinker
reflectively considers the cause of an immediately experienced
headache, the neural mechanisms of binocular vision, or a solution to
the mind–body problem. It is the occurrence of such reflexively inten-
tional relations that we experience as self-consciousness, and that may
ultimately constitute our sense of self.
God, a divine supernatural
11 mind?
Concepts of God
An enquiry in applied scientific ontology into the existence or non-
existence of God is not guaranteed to agree with the attitudes of
religious faith. We want to know whether God is an individual divine
entity, or a host thereof if there are many gods, just as we want to
know whether there are numbers, sets or universals. The difference is,
among other things, that God is a person, or the gods are supposed to
be persons, or at least personifications of natural forces, whereas
numbers and everything else in the existence domain other than
minds is assumed to be impersonal, non-mental, non-psychological,
non-intentional. It is appropriate, therefore, to consider the ontic
status of God as a sequel to the ontology of mind.
God is often supposed to be the greatest intelligent entity, an all-
powerful creator and wrathful or merciful judge of mankind. The
gods in most cultures often seem to outsiders to be open to strange
briberies. The faithful in their rapture and desperation often believe
that they can propitiate God or the gods by religious ceremonies
and sacraments in acts of piety, to influence divine intervention in
the course of their lives. Not unexpectedly, the vast variety of
devout practices involve projections of human values, attitudes and
expectations onto the idea of a divine entity or entities, by which
customary modes of tribute to reigning secular authorities in a local
power structure, showing honour to family and community
members and rulers, are deemed appropriate also for the worship of
a divine entity or entities. Whatever the ontic status of polytheistic
pantheons, the prevailing monotheistic idea of God as an all-know-
ing, all-powerful and perfectly benevolent being, whatever its
anthropological origins and however satisfying it may be for believ-
ers to contemplate the existence and will of God as a centre for
254 ONTOLOGY
their spiritual lives, raises profound philosophical questions in
applied scientific ontology.
1
We shall try to gain some perspective on the problem of whether
God, as conceived in monotheistic religious traditions, exists or does
not exist. We shall ask, without assuming that our conclusions need
detract from the extraphilosophical faith and religious commitment
of the adherents of any religion, whether God, along with physical
and abstract entities, and the finite minds of intelligent animals such
as ourselves with their combined physical and physically irreducible
properties, should be included in a preferred existence domain, or
whether philosophical reasoning, as far as it takes us, suggests the
opposite conclusion instead, that God does not exist. At no disadvan-
tage to the drama of an enquiry in which many persons have a very
deep and personal stake, we can preview the outcome of the combina-
torial ontology we have been developing as casting grave doubt on the
possibility of God’s existence.
It may nevertheless be possible to superadd God to a religiously
preferred applied non-scientific ontology under a different meta-
physically less problematic description of God’s property combina-
tion as a divine supernatural mind that is not omnipotent, omniscient
and perfectly benevolent. The option restores a modified notion of
God to the ontology. Such an idea of God is admittedly unlikely to
appeal to most believers, even if they are willing philosophically to
grasp at such conceptual straws, because it requires significantly
watering-down the properties that are often thought to be necessary
in order for God to be worthy of worship.
Scientific ontology and religious faith
The prospects for rigorously demonstrating the existence of God
have never been encouraging. Many people who believe in God have
not reasoned the matter out, but feel in their hearts that God exists
and can answer prayer. Others are likely, without attempt at proof,
to follow, through their lifetimes, the religion in which they were
raised as children, especially if their beliefs are closely connected
with their sense of ethnic or other social identity. A religion is first
of all a subcommunity of persons associating to worship something
divine. There is nothing necessarily wrong with persons of religious
faith gathering for meditation and ceremony and renewal of
faith. Such elements of religious belief have nothing positive to do
with the problem of God’s existence as it comes under the scrutiny of
applied scientific ontology. Theology is different from faith and
GOD, A DI VI NE SUPERNATURAL MI ND? 255
scientific ontology, and philosophy of religion is something else yet
again.
What is the application of combinatorial ontology to the question
of the existence or nonexistence of God? There are two related issues.
One is the problem of whether the combinatorial analysis of being
offers any special advantage in the effort to provide a good philo-
sophical reason to believe in the existence of God. Should we include
or exclude God from the preferred theoretical existence domain? We
must, secondly, look at the problem of God from the standpoint of
whether the combinatorial analysis of existence as maximal consist-
ency suggests any special reasons not to include God in the preferred
existence domain. When the smoke clears, it is evident that there is no
good reason to believe that God has a maximally consistent property
combination, from which it follows on the combinatorial analysis of
being that there are grounds for disbelieving in God’s existence. If
God is a fictional object, according to the combinatorial analysis, then
the concept of God is, inclusively, either predicationally inconsistent
or incomplete. There are indications of both of these ontic failings in
God’s property combination that raise doubts about the existence of
God as a divine supernatural mind. The idea that we might need to
suppose that God exists in order to account for the existence of the
actual world or to satisfy the demands of justice for unrectified
wrongs or unrewarded acts of righteousness, incurred during our
human lifetimes, are equally discredited in a combinatorial ontology.
What is left for philosophy of religion in applied scientific ontology
is philosophical theology. We can cast religious feeling into philosophi-
cal language as many writers in this field have done, from ancient times
to the medieval church metaphysicians to Søren Kierkegaard, Reinhold
Neibuhr, Paul Tillich and many others. We should equally include
contemporary prominent hard-minded analytic philosophers of religion
who approach the subject with a prior commitment to the truth of
religious beliefs before they try to answer even the most basic philo-
sophical questions about the existence or nature of God. If we impose
the same standard on God and the gods as we did in the case of other
putative entities we have considered for possible inclusion in or exclu-
sion from a preferred existence domain, then we must admit that the
best arguments disprove rather than uphold the existence of God, and
that there is no reasoning that establishes the existence of God as a likely
implication of the combinatorial analysis of being. The deeper trouble
in a conscientious application of Ockham’s razor is that we need not
bring God into the explanation of the existence or any aspect or
property of the actual world in combinatorial ontology.
256 ONTOLOGY
Divinity through an ontological glass, combinatorially
An actual world must actually exist, as we have argued, as a logical
combinatorial necessity. Thus, we do not need the existence of God in
order to explain why there exists a physical material universe, a some-
thing rather than nothing. Nor do we need to assume the existence of
God in order to understand why the particular facts of the actual
world exist precisely as they do. Partly the answer is combinatorial
roulette; partly it is the inexorable effect of cause and effect on the
material entities of the physical world, stirred up less predictably by
the intervention of human thought and action, and, as we have
suggested, by the contra-causal freedom of intention.
If God exists as a mind, and if some divinely modified property
dualism is a correct philosophy of mind, if, that is, a mind divine or
mundane must be an entity with intrinsically intentional properties,
then presumably we must suppose that God has at least the same free-
dom of intention as ourselves, by virtue of the intentionality of God’s
divine thought. If not, then either God is not a mind or we have not
yet adequately understood the concept of mind. Only the latter alter-
native can possibly help the philosophical theist. Nobody wants to
allow that God could exist merely by virtue of being an abstract entity
like the number r, but only as a thinker, a world designer, creator,
judge. Whatever else God is or is not, God like ourselves is a con-
scious being; not a hunk of rock or wood, not even the sun or wind or
rain, or whatever people sorely need more or less of wherever they are
trying to live.
If God is a divine supernatural mind, does God exist in time, and
hence, like all other spatiotemporal entities, is God subject to change?
Can God get old? What if God were just as old as the universe and
comes into middle age during some part of our occupation of its
lifecycle? What if, eventually, after billions and untold billions of
years spreading out over billions and untold billions of light-years of
intergalactic space, God gets old and dies, like all things with minds
presumably do, without ever noticing that the world his infant
thoughts created contains advanced primates capable of reasoning
about God? On this analogy, even if God exists, God has no idea of
our existence as thinkers, despite the assumption that God sees what
humans build as great cathedrals and mosques and synagogues,
humble neighbourhood houses of prayer and bedside shrines. Does
God know that he, she or it is being worshipped? Does God even have
anything like the human concept of worship? If God looks down from
heaven, can God understand our thoughts any better than we can
determine what a friend is thinking in observing her behaviour? If we
GOD, A DI VI NE SUPERNATURAL MI ND? 257
believe that philosophy of religion depends on the inclusion of God in
the preferred existence domain, then philosophy of religion does not
have much of a combinatorial leg on which ontically to stand.
God and Ockham’s razor
It is worth reflecting on the fact that we have already completed at
least in outline a philosophically coherent and in many ways
commonsensical ontology without ever having appealed to the exist-
ence of God. Logically, as far as classical logic takes us, it is either true
that God exists or that God does not exist. If we do not need to
include God in the ontology, if we can complete the project of pure
and applied ontology without assuming that God exists, then the
concept of God from an explanatory standpoint is philosophically
bankrupt, however spiritually rewarding.
We cannot say whether or not God has being from the standpoint
of either physical or abstract entities. The physical sciences do not
reveal the existence of God; theological–metaphysical but philo-
sophically unsupported speculations by justly renowned physical
scientists aside. Nor is God included in the subdomain of abstract
entities in a minimalist existence domain ruled by Ockham’s razor. If
we are correct in thinking that a philosophically coherent and
commonsensical ontology can be hammered out without presuppos-
ing the existence of God, then God fails Ockham’s requirement. This
does not mean that God does not exist, but that for philosophical and
scientific purposes we do not need to suppose that God exists. If we
believe in the existence of God, but are trying to avoid epistemically
unjustifiable appeals to revelation and faith, then we must find a good
previously overlooked reason why we would absolutely need to
include God in a preferred existence domain.
Alternatively, we can regard God, defined as something less than all-
powerful, all-knowing and perfectly benevolent, as a detachable part of
the ontology optionally available for those who choose to believe. Athe-
ists, if they are right to disbelieve in the existence of God, have no need
to dispute with believers, who for their part accept an ontology that on
top of everything else also includes God. Believers who bring in God as
an add-on to the ontology need not offend tolerant disbelievers who
accept a more economical preferred existence domain that excludes
God, while anthropologists can try to explain the religious activities,
rites and rituals of believers whether or not God actually exists.
Many powerful world religions have not always found it necessary
for their religious beliefs to include belief in the existence of God or
258 ONTOLOGY
gods. Classical Buddhism does not worship the historical Buddha as a
god. Nor need a true Buddhist believe in reincarnation, if the core of
Buddhist teaching is the Buddha’s struggle to achieve enlightenment
in this life. There is a school of Buddhism that interprets the Buddha’s
awakening to truth as consisting in his compassion toward the suffer-
ing of others. The Buddha solves a long-standing religious riddle,
without acknowledging the existence of God or gods, by concluding
that we escape the wheel of dharma and attain nirvana, ending the
perpetual cycle of birth, death and rebirth, by recognizing that the
soul can be laid to rest after the death of the body in this world
because there is no afterlife with which we need be concerned. This,
too, is a religion that offers its adherents peace of mind, of a very
different sort from that of worshippers who desire eternal life and
dread the annihilation of their personal psychologies.
With respect to other world religions that presuppose the existence
of God, questions persist about the relation of ontology to religious
beliefs. Is it possible to settle the question of the existence of God
philosophically? If not, then we should probably leave matters of
religious belief out of consideration in ontology, beyond allowing that
believers who so choose can tack on a truncated concept of God to the
existence domain of applied ontology, as, for example, a divine very
powerful benevolent mind, in defiance of Ockham’s razor.
God, as usually conceived, cannot be classified in any of the three
established subcategories of physical, abstract or subjective psycho-
logical entities. We have defined the concept of mind as a dual-aspect
entity, partly physical and partly non-physical, the qualia and inten-
tionality of whose thoughts supervene on a neurophysiology or other
appropriately complex physical structure. Even taking into account
the emergence of animal minds in terrestrial evolution, we refer only
to physically embodied living biological–social organisms capable of
producing thoughts with experienceable mental content and refer-
ence to intended objects. God could be included in the existence
domain as it stands only in a special category of psychological entity,
a mind that is first of all pure spirit, not a dual-aspect entity super-
vening on or emerging from a physical foundation, that additionally
has all the remarkable properties required to fulfil worshippers’
expectations of a creative sustaining compassionately judging perfect
being, a divine entity, incapable, presumably by virtue of possessing
all perfections, of undergoing any sort of real-time change.
We can, in principle, make such an exception in applied ontology
for a particular type of being, but only with sufficient philosophical
justification. That, however, is just the problem in considering the
GOD, A DI VI NE SUPERNATURAL MI ND? 259
existence of God. Adequate reasons to support a special order of
existence for a purely spiritual entity are conspicuously lacking. We do
not experience God in sensation, nor can we imagine God as an
abstract entity. Up to this point we have equated physical with
spatiotemporal entities, and abstract with non-spatiotemporal entities.
If God exists, then God apparently must be non-spatiotemporal despite
being non-abstract. To invent an entirely new category for the sake of
maintaining God’s existence in applied ontology seems unwarranted in
view of the failure of the concept of God to meet the explanatory
necessity criterion of Ockham’s razor. This is not to say that even some
of the most unpromising lines of argument for the existence of God do
not have occasional enthusiastic adherents. Using philosophy to try to
bolster pre-established faith in God intellectually is nevertheless quite
another thing than open-minded ontological enquiry that looks
candidly into the philosophical question of whether God exists and
follows only the best arguments wherever they lead. Philosophy of
religion, like any other branch of ontology, should be a mode of
enquiry rather than a way of dressing-up prejudices about how we
hope and want certain answers to come out. If we adopt the attitude
toward philosophical reflections on the ontic status of God, then it is
hard to see how applied ontology is ever going to offer much aid and
comfort to religious believers.
Arguments for and against the existence of God
If God’s being could be rigorously demonstrated, then the conclusion
that God should be excluded from a preferred existence domain on
the strength of Ockham’s razor would plainly need to be rethought.
However, there is not only a dearth of good arguments to prove the
existence of God, but solid reasons for doubting, especially from the
standpoint of a combinatorial analysis of the concept of being, even
the logical possibility that the God of monotheism could exist.
The combinatorial analysis of being undermines the argument that
God must exist in order to explain why there is something rather than
nothing. It substitutes a logical combinatorial explanation in place of
God as a divine supernatural being that wills the existence of the
world. The cosmological proof and the argument from design for the
existence of God are thereby refuted in a single turn. The so-called
ontological proof for the existence of God also fares badly in combina-
torial ontology. To conclude that God exists because God by defini-
tion is supposed to be the greatest conceivable being, and that if God
did not exist we could conceive of a being greater than God, one that
260 ONTOLOGY
was actually a being or that actually existed, is disallowed by
combinatorial pure philosophical ontology.
The identifying properties by which objects are considered as
possible candidates for inclusion in a preferred existence domain are
limited to constitutive properties that do not entail an object’s ontic
status as existent or nonexistent. The reason for the requirement is
that otherwise we cannot say of the very same object that it exists or
does not exist, because we change the identity of the object if we
include the properties of existing or not existing in its individuating
property combination. This restriction restates Kant’s conclusion in
the section of the Critique of Pure Reason on “The Ideal of Pure
Reason”, in which he criticizes the ontological argument for its
consideration of existence as a perfection, or as any kind of “predi-
cate”. The same objection precludes the evaluation of a property com-
bination as predicationally complete or incomplete, consistent or
inconsistent, on the basis of whether or not it includes the fact that an
object exists or does not exist. If existence and nonexistence are
properties but not identity-determining constitutive properties or
“predicates” in Kant’s sense, then we cannot validly conclude that
God as the greatest conceivable being necessarily exists. We cannot in
that case rely on the inference that we can conceive of a being greater
than God, when we assume for purposes of indirect proof that God
does not exist.
2
We are left with only the so-called moral argument for the existence
of God. God must exist, according to this way of reasoning, in order
to right the wrongs undergone by human beings in their brief life-
times, in an eternal afterlife of reward or punishment. The argument
projects a period of survival of the person after the destruction of the
body that endures long enough to sort out whatever earthly injustices
have occurred. The demands of justice logically require that God exist
in order to manage the meting out of rewards and punishments in a
continuation of the mind’s existence beyond death.
3
The moral argument seems to depend more on emotional wishful
thinking than good judgement. That there are injustices in this life no
one need dispute. Why suppose, however, that injustices will ever be
redressed in an afterlife, or that God must exist in order for justice to
be dispensed? What if there were an afterlife in which perfect moral
harmony and accord were achieved for persons who did wrong and
were never punished during their lives, and for persons who did good
and were never rewarded, and all the scales evened out and balanced
perfectly after a couple of millennia, but there was no God overseeing
the process? What if things just happen this way through the playing-
GOD, A DI VI NE SUPERNATURAL MI ND? 261
out of abstract principles of justice, the moral equivalent of natural
laws, or, perhaps as further consequences of natural laws themselves?
What reply can then be made on behalf of the moral argument specifi-
cally as an effort to prove the existence of God? Then again, why not
simply conclude, as a fact of life that all but the most naive among us
should eventually with mature vision come to accept, that some
people are destined to enjoy the fruits of wrongful gain without ever
being punished, while others, usually the innocent inoffensive ones
among us, are as often as not cosmically screwed? Why should the
actual world not be that way? Not from any reason we can extract
from combinatorial pure philosophical or applied scientific ontology.
Why suppose that injustices will ever be made right?
The problem of evil poses a positive and still unanswered challenge
to the possible existence of God. If God is the creator of the actual
world in which, as we all too plainly see, natural evil abounds, then,
paradoxically on the traditional monotheistic concept, God does not
know about the evil, or is insufficiently powerful to prevent it, or
lacks the requisite good will to do so. Any of these three possibilities
contradicts the definition of God as all-knowing, all-powerful, and
perfectly benevolent. If the concept of God harbours such an evident
predicational inconsistency, then the combinatorial analysis of being
as predicational maximal consistency entails that God not only does
not exist, but logically cannot possibly exist. The existence of such a
God is tantamount to attempting to gain admission to the preferred
existence domain of a more blatantly predicationally inconsistent
nonentity like the round square or carnivorous vegetarian. Philos-
ophers and theologians have wrestled with this problem, and intro-
duced the field of theodicy as a branch of philosophy of religion to try
to solve it. Many critics continue to believe that all efforts to rectify
God’s existence as a perfect being with the glaring imperfections of
the world of God’s creation are abysmal failures. The reaction of
some philosophically conscientious believers in light of the problem
of evil is to relax the three-part definition of the concept of God to
allow God as all-knowing and perfectly good, but not necessarily all-
powerful in the sense required to prevent all natural evil, or to
compromise on some other diminution of the traditional attributes of
divinity. The problem of evil is avoided in this way only by abandon-
ing the full majesty of God as it has usually been conceived.
4
Along with problems about the predicational consistency of God,
construed in the first instance as a logically possible object with a
property combination containing the properties of being all-knowing,
all-powerful, all-good and the creator of a world rife with natural evil,
262 ONTOLOGY
there are concerns also about God’s predicational completeness.
Some theologians have postulated that, in addition to being omnipo-
tent, omniscient and perfectly benevolent, God must also be omni-
present, existing everywhere at once throughout the universe, while
others have argued that God must transcend the actual world. We
have already seen that transcendence and transcendent entities are
incompatible with the combinatorial theory of being as maximal
consistency. If the argument against transcendence in a combinatorial
framework is correct, then we cannot expect to make sense of the idea
that God is a transcendent entity.
What else can anyone be said to know about God, about God’s prop-
erties? Do we know enough to suggest both predicational consistency
and completeness in God’s constitutive property combination? We
know at once too little and too much. We know too much, because from
the traditional concept we are thrust into the problem of evil, given the
prevalence of pain and other imperfections in God’s creation. We know
too little, because the standard monotheistic concept of God leaves
many predicational gaps in God’s property combination. We may hope
to fill in the blanks in a variety of ways as religious myths and holy texts
sometimes try to do, relying on human imagination to the best of its
limited abilities. We can also try to console ourselves that if God exists
then God’s property combination by definition must be complete, any
omissions being due entirely to gaps in our faulty finitely limited knowl-
edge. The deeper difficulty is not merely epistemic, involving our igno-
rance of God, since we do not know the complete set of properties in
the property combination of any except perhaps the simplest abstract
entities. We are more conceptually constrained by the fact that we may
not be able even in principle to make sense of the attributions of addi-
tional properties to God that would need to be maintained in order to
project a complete property cluster. We do so unproblematically in
many matters of ontological dispute, but we have no way of verifying
the accuracy of any of these enterprising conjectures about the nature
of God. We can raise such an objection in the case of an object like God,
given all the other infelicities in the concept of a divine being that we
have already mentioned, without committing ourselves generally to an
implausible positivistic verification theory of meaning.
Inherent inconsistency of religious beliefs
A combinatorial ontology by itself does not disprove the possibility of
extending the preferred existence domain of applied ontology to
include God or other divinities. Such a superaddition can be arranged
GOD, A DI VI NE SUPERNATURAL MI ND? 263
only if God’s property combination is reconceived as maximally
consistent, any gaps owing entirely to our ignorance of God’s full
complement of properties, and, despite appearances and even
contrary to much of the driving force of religion, free of any and all
predicational incompatibilities.
Inconsistency may turn out to be ineliminable from the essential
dynamic tensions in religious beliefs by which the mind seeks
personhood, growth and fulfilment in and through religion. That
God is both three persons and one person, that a virgin should give
birth (common to Buddhism, Christianity and other religions), that
God is all-powerful and yet engaged in a struggle with the forces of
evil, that God is perfect and hence presumably unchanging and yet
amenable to petitionary prayer, together with all the credulity-
straining miracles that contradict belief in mundane causation and
natural law in most religions, in accounts of religiously significant
episodes recorded in holy writings, are among the more conspicuous
inconsistencies in religion. The inconsistency inherent in religious
belief may be vital to the spiritual awakening of the self, but testifies to
a concept of God that for better or worse is riddled with contradic-
tions, and hence excluded from the preferred existence domain by the
consistency requirement in a combinatorial analysis of being.
The idea that inconsistencies are essential to religious beliefs is
familiar in sceptical literature. The emergence and maturation of the
self into self-consciousness might actually depend on contradictions. It
is perhaps only in this way that thought is supplied with the necessary
motivation to sort out conflicting beliefs, riding the conflicts between
and working its way through logically inconsistent commitments, to
attain a higher perspective in which at least some of the contradictions
are resolved and an equilibrium of religious outlook is achieved.
The emphasis especially in evangelical Christianity on the renewal
of faith as a kind of spiritual rebirth in which the believer’s soul is born
again is an explicit but by no means unique instance of a more perva-
sive aspect of religion, in which the self comes to be more clearly self-
consciously defined as a result of its assimilation of inconsistencies
within religious doctrine.
5
If the religious self arises as a result of strug-
gling, even if only subconsciously, to incorporate contradictory beliefs
into a unified worldview, then the sort of logical inconsistencies often
attributed to religion as a criticism and rebuke of its doctrines can be
seen instead in a different light. They are not then automatically a sign
of the failure of religion, but the source of its strength and influence in
a believer’s sense of self in relation to the concept of something much
greater than the self and its puny methods of reasoning. It is in the
264 ONTOLOGY
effort to resolve inconsistencies in religion, especially as they reflect
deeply grounded contradictions in the concept of God, trying to
understand the nature of God as good despite the natural evil in the
world, among innumerable similar conceptual discords, that the
religious self more fully emerges.
6
To the extent that even one logical inconsistency remains unre-
solved in the idea of God, despite the value of contradictions in reli-
gious life, the combinatorial analysis of being as maximal consistency
must deny that God exists. Regardless of how personally fulfilling and
emotionally supportive it may be for many persons to accommodate
predicationally inconsistent concepts in their belief systems, the
judgement of applied scientific ontology is that no such object can
possibly exist. The greatest irony of the ontology of religious belief
may then be that in order for religion to succeed, for it to offer the
satisfactions of personal development, sense of self, mystical separa-
tion from the ordinary world of empirical experience and rational
scientific and philosophical explanation, and unity with the divine,
God not only does not need to exist, but paradoxically cannot exist.
The concept of God in that case serves the most fundamental religious
needs of believers only by virtue of subsuming predicational inconsist-
encies that preclude God’s existence.
Ontology of culture: language,
12 art and artefacts
Cultures and cultural objects
We turn finally to the topic of cultural entities. The world contains not
only natural objects like rocks and plants, but objects that would not
exist as complexes or in the exact form with the particular properties
they have were it not for human intervention. There are artefacts,
products of human thought that are touched and transformed in vari-
ous ways by human hands. The list of such things includes expressions
of thought in language and art, and all the results of human invention,
manufacture and technology.
It may be significant, in this study of combinatorial ontology, an
expressly anti-Heideggerean anti-existentialist theory of being, that we
should end up where Heidegger, relying on phenomenology rather than
logic as the key to ontology, finds it necessary to begin. We conclude the
analysis of applied scientific ontology in effect with a discussion of
Zuhandenheit and the impact of human intention and activity that
shapes and colours the world in a distinctively human way.
The applied ontology of cultural entities that we shall sketch for
simplicity is limited to human culture. We should recognize at the same
time that other terrestrial non-human animals also have more restricted
social cultures, and in less extensive ways also change their environ-
ments by making artefacts and assembling composite entities out of
available materials to suit their needs. A nest in a tree, damming a river
to make a lodge, even a tunnel in the earth, are cultural artefacts of a
crude sort. Nor should we discount the possibility, even the statistical
likelihood in the turn of combinatorial roulette that has resulted in the
realization of the actual world on the present theory, that in the vast
distances of space there might exist other life forms, extraterrestrial
beings with intelligence, even advanced civilizations very unlike the
human cultures we know. The ontology of language, art and artefacts
266 ONTOLOGY
that we require must be fully general with respect to such possibilities,
even if the theory is most conveniently illustrated with examples drawn
exclusively from human culture, exemplifying what is most near and
dear to us, that we are best able to study and comprehend.
As a further provision, we distinguish between language, art and
artefacts, even though there are proposals for reducing these three
categories to two or even one, and that in different directions. Thus,
one might say that language and art are special kinds of artefacts, so
that the ontology of culture need only concern itself with the making
of things, imposing human design on tools and weapons, shelter,
clothing, objects of religious worship, agricultural and other modifi-
cations of the environment, including art and language more
narrowly understood. Or language and artefacts might be reduced to
art, in which we speak of the art of expressing ourselves verbally, the
art of war, architecture, body covering and adornment, the art of
farming and so on. We might concentrate categories in yet another
way again by speaking of art and artefacts as a kind of language, of
which verbal expression, spoken and written language in the ordinary
sense, is but one subcategory.
Whatever the prospects of these reductive programmes, it is clear
that the three types of cultural entities – language, art and artefacts –
are the principal subjects of consideration, however they may turn out
to be interrelated. We do not want to prejudge refinements of the
ontology of culture that may lead to more reductive characterizations
of its preferred existence domain. We proceed accordingly as though
our cultural data for ontological reflection came prepackaged in
discrete categories for language, art and (other kinds of) artefacts,
even if these should turn out to be more economically categorizable as
expanded subdomains or as a single more expanded domain. We can
begin at least by recognizing the fact that the entities to be discovered
in the actual world are different because of the activity of intelligent
agents, minds, both human and non-human, and that at their most
sophisticated adaptations known to us, so-called cultural entities
feature prominently at a certain arguably superficial level of analysis,
in the form of language, art and artefacts. With these conspicuous
phenomena we can begin to uncover the basic principles of an applied
scientific ontology of culture.
Ontic status of culture
The first question we confront is why cultural entities should be
considered as constituting a special ontic subdivision. The healthy
ONTOL OGY OF CUL TURE 267
sceptical impulse that restrains metaphysical extravagance by invok-
ing Ockham’s razor might naturally want to raise doubts at the outset
about the validity of introducing an ontology of culture.
We have seen in general terms that Ockham’s razor is not an
absolute criterion in ontological investigations, and that the proper
use of the principle requires care if it is not to mislead enquiry. Still,
every application is a unique case, and it is at least worth wondering
whether or not cultural entities are already properly subsumed under
the previously established categories of physical, abstract or subjective
psychological entities, or whether they require an applied ontological
subdomain all their own. A good, but perhaps not very convincing or
ultimately satisfying, argument can be made for both the simple inclu-
sion of cultural entities as physical or abstract.
Let us consider an example of a putative cultural entity from each
of the three ostensible categories we have introduced, to ask whether
there is any justification for classifying such objects as ontologically
distinct in any meaningful way from the workhorse ontological
divisions we have already recognized for physical, abstract and subjec-
tive entities. As specimens, we introduce a spoken or written sentence
of a language, a neolithic cave painting of a buffalo pierced by an
arrow, and a tool, say, Heidegger’s hammer, or a computer, or the
space shuttle or International Space Station. These are all things that
are made, and in our limited perspective taken for purposes of illus-
tration, made by human beings, either as individuals or in cooperating
social teams, using language and other tools and artefacts along the
way among other devices to coordinate their complex activities,
resulting in the production of cultural entities. We have already
remarked that such entities are not natural. The question is, are they
simply or purely physical entities, belonging to a subcategory of
artificial physical entities alongside and hence not deeply onto-
logically distinct from natural physical entities? Or are they instead to
be classified as or understandable in terms of abstract entities?
When a sentence is uttered or written, whether with pen and ink or
chiselled into stone or inscribed by means of a pattern of magnetic
traces on the surface of a plastic computer diskette, it is in some obvi-
ous sense a physical entity. It might also be said at the same time to
represent an abstract meaning, the proposition, as we have encoun-
tered the term in our consideration of the subcategories of abstract
entities, if we were to include propositions in the ontology. Much the
same can be said of the cave painting or the hammer, computer or
space station. These entities too, in different ways, can be thought of
as embodying abstract relations, particularly in the case of the cave
268 ONTOLOGY
painting and the computer, but even by extension, if we stretch things
far enough, in the hammer and the computer-assisted design and
operation of the space shuttle and space station. As responsible
ontologists, we should not try to maintain that the sentence, painting,
hammer, computer or space station are themselves abstract entities,
since all of these things are undeniably here with us in real spacetime
in the actual world, whereas abstract entities are supposed to be non-
spatiotemporal. We might nevertheless try to skate by with our two
established categories of physical and abstract entities by classifying
cultural entities of any or all three types as physical entities embody-
ing or manifesting certain special types of abstract properties, ideas,
concepts, formal relations or the like, and thus dispense with the need
to go beyond the ontology of physical and abstract things in order to
account for the metaphysics of culture. Would such an analysis of the
ontology of language, art and artefacts be satisfactory?
There is an argument to suggest that cultural entities cannot simply
be subsumed beneath the pure categories of physical and abstract
entities, no matter what other explanatory advantages they afford.
The objection for good reason is parallel to that offered in attempts to
solve the mind–body problem, of which the question of the ontic
status of cultural entities can be seen as a particular related instance.
The claim is that we cannot fully understand language, art and
artefacts, cultural entities generally, except as expressions of the
qualia and intentionality of thought. This is perhaps most clear in the
case of language used as a vehicle for recording and communicating
sensations, emotions and ideas, but equally so in all of art, even the
most modern abstract or supposedly non-representational art.
Derivative intentionality of artefacts
Although artefacts other than language and artworks in the narrow
sense are not more obviously expressions of propositional meaning,
they are nevertheless, as Heidegger among others rightly recognizes,
thoroughly intentional. Their design, manufacture, and use are alike
directed toward and embued with human purpose.
If I fashion a hammer by selecting a particular river-smoothed stone
and fastening it with leather thongs to a wooden heft, I am choosing,
shaping, assembling and finally using physical objects in my immediate
environment with a certain end in mind. A boulder will not do if the
hammer is supposed to be used as a practical tool; that would make it
too big and heavy, whereas I must be able to lift it up and swing it down.
A chunk of sandstone will also probably not serve (although I might
ONTOL OGY OF CUL TURE 269
experiment with any variety of substances until I identify appropriate
materials for my purposes) because it will too easily shatter if I use the
hammer as I am likely to want to in striking harder objects. When the
hammer is made, no matter how ineptly, imperfectly or incompletely,
it represents, as much as any speech act or artwork, a mind’s intentions
and the attempt to fulfil those intentions by acting in and locally ma-
nipulating aspects of the physical world in the service of an idea, in the
partial fulfilment of an intention.
Minds and their concrete expressions in language, art and artefacts
can be classified, accordingly, not as purely physical or purely abstract
entities, but as qualia-expressive intentional entities, being in every
instance about something or directed toward an intended object. The
intended object of a use of language, or the production or display of an
artwork or other artefact, is often to express the qualia of a thinker’s
thought. To paint a canvas or write a letter or sing the blues is to clarify
for oneself and make available to others a record of the content of one’s
psychological states. Cultural entities are not themselves minds, natu-
rally, and if they embody or otherwise manifest thoughts they are not
themselves mental occurrences. Here an important division between
two kinds of intentional entities can be adduced in the applied scientific
ontology of cultural entities, based on a distinction first drawn by John
R. Searle in his book, Intentionality: An Essay in the Philosophy of Mind,
between intrinsic and derivative intentionality.
1
It is obvious enough, but bears reminding, that were it not for the
existence of minds there would and could be no culture. Language,
art and artefacts are products of thought, in all instances their direct
expression in physical form. The same is true whether we are refer-
ring to a single sentence uttered by an early hominid or all of world
literature, a cave painting or the œuvre of Michelangelo or Salvador
Dali, a stone hammer used to crack oyster shells or the International
Space Station. If, as we have argued, we cannot solve the mind–body
problem except by recognizing the physically ineliminable and irre-
ducible qualia and intentionality of thought, and if qualia and inten-
tionality require a special applied scientific ontological category of
minds as qualia-bearing intentional entities in addition to and distinct
from physical and abstract entities, then how can we hope to under-
stand the metaphysics of culture and the ontology of language, art and
artefacts, except as products of thought, sharing in some way in the
qualia and intentionality of thought whose properties uniquely
characterize the ontology of mind?
An intentionalist philosophy implies that cultural entities, like the
minds that through physical agency produce them, are intentional
270 ONTOLOGY
entities, and as such require a special category of the preferred
existence domain distinct from physical and abstract entities.
Cultural entities have physical and abstract properties, just as physi-
cal entities have abstract properties and enter into abstract relations,
like the abstract property of being divisible or atomic. We may
accordingly consider the three-part applied scientific ontology that
emerges in the discussion of the mind–body problem, consisting of
physical, abstract and qualia-bearing intentional entities, to be suf-
ficient also for cultural entities, without interposing yet another,
fourth, category of existent things. The explanation of thought in
language, art and artefacts is intentional in the correct sense of the
word in so far as these cultural entities are about something or
directed toward an intended object, and expressive of the content of
a state of mind.
The sentence “It is raining” is about a meteorological state of
affairs, and ordinarily expresses a belief that the state of affairs
obtains. It is true or false, moreover, depending on the actual state of
the world, the existence or nonexistence of the corresponding state
of affairs the sentence is intended to represent and the belief it is
meant to express. The cave painting is about the buffalo depicted,
real or imaginary, and the state of affairs, existent or otherwise, of its
being struck by an arrow. It may represent the fears of the artist, the
hope for a successful hunt, or something of more metaphorical or
religious significance as a cult object. The possibilities, thanks to
conventional symbolism and psychological association, and the
logical detachment of the content of thought from its intended
objects, are potentially limitless. The same analysis explains the
collective intentionality that stands behind social institutions such as
customs, etiquettes, religious and secular observances, mating and
marriage, the use of money as a medium of exchange and all other
aspects of culture.
Artefacts as embodied purpose
An artefact like a hammer, computer or space station is likewise the
expression of purpose, of varying degrees of complexity, but equally a
product of thought and concrete embodiment of the idea or ideas of a
mind or many minds acting in concert intentionally and for the sake
of realizing an intention. We can often grasp shared or imaginable
purposes directly from the object, and even when we are wrong in our
assumptions, it is significant that we find it irresistible in such cases to
see the work of mind in the creation of such things.
ONTOL OGY OF CUL TURE 271
Thus, a hammer is about hammering, about the things its makers
and users intend to do with it. Similarly for much more complicated
and sophisticated instruments like a digital computer or the space
station. To such an extent is intentionality inherent in a purposeful
artefact that, even when a tool or like object, a hammer or a cup or
bowl, becomes so damaged that it is no longer able to fulfil its
function, the entity does not simply return to nature, at least not
immediately, but, as Heidegger charmingly puts it in Being and Time,
even on the rubbish heap, it “bids farewell” to we thinkers and
makers. Heidegger’s remarks on the evidence of care in broken imple-
ments are worth considering at length:
Beings nearest at hand can be met up with in taking care of things
as unusable, as improperly adapted for their specific use. Tools
turn out to be damaged, their material unsuitable. In any case, a
useful thing of some sort is at hand here. But we discover the
unusability not by looking and ascertaining properties, but rather
by paying attention to the associations in which we use it. When
we discover its unusability, the thing becomes conspicuous.
Conspicuousness presents the thing at hand in a certain unhandi-
ness . . . In its conspicuousness, obtrusiveness, and obstinacy,
what is at hand loses its character of handiness in a certain sense.
But this handiness is itself understood, although not thematically,
in associating with what is at hand. It does not just disappear, but
bids farewell, so to speak, in the conspicuousness of what is unus-
able. Handiness shows itself once again, and precisely in doing so
the worldly character of what is at hand also shows itself, too.
2
The cup, dropped on the floor and broken in two, unable to hold
tea, still “says” that it was once something useful, something intended
for a specific use, capable in its glory days of fulfilling a practical
purpose. We can read intentionality even into a ruined artefact, as
when we visit the sites of abandoned ancient cities like Macchu Picchu
or Aphrodisias. Here we see clearly a large-scale object that is not
merely a work of nature, the result of natural forces acting at random,
but an artefact first shaped in thought and then fashioned by hand or
with the help of other tools or machines by many persons in a
relatively advanced state of technology. Against the background of
nature, these creations stand out dramatically in what Heidegger calls
their conspicuousness (Auffälligkeit).
We might also reflect in this connection on how the trained
archaeologist and anthropologist is able (fallibly) to distinguish
272 ONTOLOGY
between natural objects and human-made artefacts that to the
layperson’s unskilled eye seem indistinguishable. A good example is
the flint scraping tools that are hard to discern from the flakes of
flint that may have splintered from a block through entirely natural
processes. An expert can identify flint scrapers from flint flakes
occurring without the hand of a human toolmaker deliberately
guided by intention and purpose with a certain end and a certain
standard in mind. It is not an occult practice, but a rather exact
science, to distinguish such tools and tool fragments from naturally
occurring shards of identical stone. The tricks of the trade can be
taught to virtually any patient novice, so that it becomes possible
also to see, as specialists do, the subtle distinctions between natural
and early human cultural entities.
We discriminate between multiple subcategories of physical
objects. There are physical forces, fields, and micro- and macro-
physical entities, particles and complexes, molecules and atoms and
the like. We similarly distinguish between multiple subcategories of
abstract entities, particulars like numbers and sets, and universals such
as properties, qualities and relations. In the third main ontological
category of qualia-bearing intentional entities, we may similarly find
it expedient, following Searle’s valuable distinction, to acknowledge
separate subcategories for intrinsically intentional entities, minds as
originating sources of qualia and intentionality, and derivatively
intentional and qualia-expressive entities, including all cultural
entities, language, art and artefacts. Derivatively intentional cultural
entities are about something or expressive of qualia only by virtue of
having been chosen by thought as a medium for the derivatively inten-
tional expression of intrinsically intentional meaning, thought and
purpose, sensation, emotion, desire and will.
All intentional entities, minds and cultural entities alike, are about
something in different ways. They can intend something by virtue of
themselves alone or by virtue of being used by thought as an expres-
sion of another intentional entity’s intentionality. The main point
from an applied scientific ontological perspective is that intrinsically
or derivatively intentional entities cannot correctly be ontically
classified as purely physical or purely abstract entities in a preferred
existence domain, but require a third main category of their own – the
category of intrinsically or derivatively intentional qualia-bearing
entities, to which minds and cultural entities generally belong. Things
that are made by minds, whether in language, art or as other kinds of
artefacts, are not simply physical entities with abstract properties, but,
like the mind on a property dualist ontology of psychological
ONTOL OGY OF CUL TURE 273
phenomena, exhibit both a physical and non-physical aspect, express-
ing the contents and intended objects of thoughts.
Even the broken teacup speaks to discerning eyes as having
another, special, kind of property, a former purpose, a former use,
ministering to an intention that cannot in turn be adequately under-
stood in terms of its physical or abstract qualities and relations alone.
It partakes derivatively of the intrinsic intentionality of thought to
which it owes its existence, and as such is not purely and not merely a
physical entity. It is for the same reason that the mind itself on the
property dualist conception is not purely and not merely the body, the
neurophysiology of brain and nervous system integrated into the
somatic matrix of a living psychological subject. If cultural artefacts
are as much dual aspect entities as the minds that create them, then,
like the mind, they require special provision in a third main category
of a preferred existence domain. The world of culture, as Karl R.
Popper, in Objective Knowledge: An Evolutionary Approach, for quite
different reasons, has also maintained, is a third distinct ontological
realm, a World 3.
3
The subdomain of cultural entities constitutes a
third world as a distinct classification within applied scientific ontol-
ogy. Physical, abstract and intentional entities exist in the combinato-
rial analysis of the concept of being as maximally consistent property
combinations, including physically and abstractly irreducible deriva-
tively intentional and qualia-expressive properties.
Abstract qualities of art
It might be thought that while the plastic arts like painting and sculp-
ture are readily absorbed into the category of physical entities in the
existence domain, other so to speak more formal or mathematical arts
like music and even poetry and literature might be taken without
residue into the category of abstract entities in the preferred existence
domain of an ontology of culture.
To consider only music, as offering perhaps the strongest argument
for this type of ontological reduction, it is clear that music is not only
the abstract relations that it exemplifies but tone qualities, rhythm
and tempo in real time, and, more importantly, expression and
expressiveness that is evidently an intentional property originating
with the intrinsically intentional qualia-bearing thoughts of compos-
ers, conductors and performers, intended to be received and to elicit
certain qualia and intentional psychological responses in an audience,
that cannot be adequately reduced to or explained in terms of the
music’s abstract mathematical forms. It is an art that speaks expres-
274 ONTOLOGY
sively from and to the human soul in a way that is not simply a matter
of abstract relations of melody and harmony, essential though these
are to the ontology of music.
The same can be said, it should be emphasized, of any art form and
of any expressive use of language or purposeful design, manufacture
or use of any artefact. An extreme example that makes an important
point about the comparative insignificance of the physical substance
chosen for artistic purposes is in so-called found-object art, in which
an artist selects and exhibits a readymade entity of no special aesthetic
quality, such as a porcelain bathroom fixture, as an expression of
choice within the conventions of an artistic community. We cannot
begin to understand the ontology of any of these cultural entities
except as expressions of the qualia and intentionality of thought, as
creations of mind, and attempts to satisfy an intended purpose. When
we recognize the expression of mental content and intention in
language, art and artefacts, then we appreciate the need to include
cultural entities in a third category of psychological or psychology-
related existents distinct from the purely physical and abstract things
in which cultural entities are embodied and whose properties they
exemplify.
4
Conclusion: scientific–
philosophical ontology
Modality of being
The problem of ontology is to understand the concept of being, of
what it means for something to exist. Ontology investigates the fact,
nature and modal status of being, in the course of which it proposes a
preferred ontology that is supposed to include all and only existent
things. To be successful, ontology must combine a correct pure
philosophical ontology with a correct applied scientific ontology,
grafting an appropriate preferred existence domain onto a satisfac-
tory analysis of the concept of being.
The proposed theoretical domain must correspond exactly with
the extant domain of actually existent entities and states of affairs that
constitute the actual world in order for the application of a correct
concept of being to be judged satisfactory in an integrated philosophi-
cal–scientific ontology. The question of precisely how the concept of
being should be understood, and whether at any point we can know
with epistemic certainty that we have brought about the positive
correlation of theory with reality, are among the difficulties that sus-
tain philosophical controversy in the field of ontology.
What, it is often deemed independently interesting to know, is the
most economical ontology needed to keep science and extrascientific
discourse afloat? If we confine our attention exclusively to questions
of scientific ontology, then we will be avoiding rather than helping to
answer the conceptually more basic questions of philosophical
ontology, and we risk doing so in violation of the more general
higher-order principles of philosophical ontology, and trying to
answer the question of what particular things and kinds of things exist
without first knowing what it means for anything whatsoever to exist.
We open the door to unnecessary confusions if we fail to distinguish
or properly observe the distinction between philosophical and
276 ONTOLOGY
scientific ontology, as when ontologists try to address a question of
pure philosophical ontology as though it were a question of applied
scientific ontology, or the reverse.
The answer to fundamental questions of philosophical ontology
require rigorous philosophical enquiry into the concepts of objects,
states of affairs and worlds, and of actually existent entities, states of
affairs and the actual world. We have taken on the difficult questions
of ontology, rather than trying to avoid them as unanswerable or even
unintelligible. The right answers to these metaphysical puzzles can
only appear when philosophical ontology precedes scientific ontol-
ogy, which as such is prohibited from appealing to any of the merely
logically contingent facts or scientific ontology of the actual world. A
correct answer to the question why there exists something rather than
nothing must in a sense be logically necessary, or, as is more accurate
but also more tedious to say, philosophically metalogically necessary.
Whatever logically necessary answer we give to the question of being
should not imply that the actual world as it happens to exist is itself
logically necessary, as we might say, in the specific details of its scien-
tific ontology.
Logic as a window on ontology
We should be reluctant to give up the logical or even physical
contingency of the actual world, and of the existent states of affairs
that constitute the actual world. It would make logic too important if
we were to interpret the facts of the world, beginning with the
descriptive facts and laws of natural science, as a matter of metalogical
necessity.
To conclude otherwise is to collapse all presumably distinct
logically possible worlds into the one and only actual world. This, to
say the least, is much at odds with our ordinary assumption that it is
minimally logically possible for particular facts of the actual world to
be other than they are. I did not have to write the preceding sentence,
or I could have edited it out, or it could have been lost at some stage
in the publication process. I, for that matter, did not have to exist, and
there are plenty of logically possible worlds in which I do not exist. If
there are abstract entities, then only their properties are universally
distributed in every logically possible world, and all other facts occur
irregularly from world to world.
Or so we think. The dilemma in trying to answer the fundamental
questions of philosophical ontology as we have approached the topic
is that of showing that, as a matter of combinatorial philosophical
CONCL USI ON: SCI ENTI FI C–PHI L OSOPHI CAL ONTOL OGY 277
metalogic, there must actually exist something rather than nothing,
while also concluding that the actual world in all its physical states of
affairs is not logically necessary but contingent.
The problem we have tried to solve is to attain both of these appar-
ently conflicting objectives by providing a logically necessary answer
to the question why an actual world exists in pure philosophical
ontology that does not also make the condition and constitutive facts
of the actual world logically necessary, preserving their presumptive
logical contingency as a subject for proper investigation by applied
scientific ontology. It is only by wending our way delicately between
these modal requirements that we can hope to satisfy the twin
burdens of ontology. We can then try to provide an analysis of the
concept of being, of why something rather than nothing exists, and
why there is a uniquely existent logically contingent actual world,
while specifying more exactly the things and kinds of things, existent
entities and states of affairs, that constitute the actual world.
Ontology demands a correct philosophical metalogic. Logic must
therefore be as independent as possible in its explicit commitment to
the principles of any particular scientific ontology. It is the implicit
ontology in logic that lurks below the surface to be excavated by
philosophical metalogic where our deepest philosophical presupposi-
tions are to be found. We have seen as a consequence of philosophical
metalogic that logically there must exist something rather than
nothing, among all the logically possible combinations of logically
possible objects with logically possible properties, if to exist is to be
predicationally maximally consistent, and that for the same reason
there can exist at most only one logically contingent actual world.
Logic answers the problems of pure philosophical ontology by
formalizing logical possibilities, true or false, of an object or number
of objects having a property.
We cannot imagine anything logically more basic than the combi-
nation of objects with properties, and hence we need not fear that the
logical analysis of being is as deeply anthropocentric in its methodol-
ogy as phenomenology. Thinking, even for non-humans, logically
requires at least implicitly attributing properties to objects, if what we
mean by a possibility is a logically consistent state of affairs, and if
what we mean by a logically possible state of affairs is the logically
possible possession of a logically possible property by a logically pos-
sible object. We are immediately involved in the principles of combi-
natorial ontology when we reflect on the ultimate presuppositions of
classical logic even in the most general sense. We have argued that it is
at this level of combinatorial possibility that logically necessary
278 ONTOLOGY
answers to the fundamental questions of pure philosophical ontology
can and must be found, and we have indicated directions in which
metaphysical enquiry into the fact, nature and modality of existence
might proceed.
Pure philosophical and applied scientific ontology
The ideal of presenting an integrated philosophical and scientific on-
tology has been held out from the beginning as the goal of these inves-
tigations. It follows as a consequence of recognizing the distinction
between pure philosophical enquiry into the question of being, and
the task of specifying what particular things and kinds of things exist
in applied scientific ontology. We need both parts of the theory to
arrive at a complete understanding of ontology, and both components
must be correctly interrelated.
The study of ontology belongs squarely to philosophy. Ontology
can nevertheless be conducted in accordance with scientific standards
of precision and intellectual rigor. There is, as we have assumed
throughout, such a thing as scientific–philosophical ontology. Now
that we have completed in outline at least the two main components
of a fully integrated scientific–philosophical ontology, it is appropri-
ate to step back and reflect on what it means to have undertaken such
an analysis, and whether and to what extent the project as a whole can
be understood as answering to both scientific and philosophical cri-
teria, by which its relative success or failure can be properly assessed.
There are several respects in which the combinatorial analysis of
being in pure philosophical ontology and the applied ontology that it
supports are scientific. Among other things, although the pure philo-
sophical component of the ontology is intended as a conceptual analy-
sis that is necessarily correct in essentials, and necessarily false if
mistaken, the applied component is revisable in many of the same
ways as ordinary empirical science. It is subject to correction in light
of new discoveries while preserving an underlying combinatorial
framework. If an unanticipated argument surfaces according to which
universals are logically inconsistent or less than maximally
predicationally complete, then the provisional conclusion of applied
scientific ontology in the combinatorial context in which we have
presented it might reasonably reverse its endorsement of the existence
of abstract entities as belonging to the preferred existence domain,
and conclude instead that universals in this subcategory of abstract
entities do not exist and are henceforth to be excluded from a
preferred existence domain.
CONCL USI ON: SCI ENTI FI C–PHI L OSOPHI CAL ONTOL OGY 279
Another important sense in which the applied ontology in the
combinatorial mode is scientific has to do with the open-ended poten-
tially unlimited expansion of ontological categories and subcategories.
As things stand, we have tentatively identified three main types of
existent entities in the preferred existence domain of applied scientific
ontology, for physical, abstract, and intrinsically intentional qualia-
bearing entities and their derivatively intentional expressions in
language, art and artefacts, with numerous subdivisions of categories
and subcategories specified within their internal ontic structures. The
expectation is that the proposed network of ontic categories and
subcategories is adequate to our present understanding of the ontologi-
cal needs of science, the kinds of things that exist given what we now
believe ourselves to know about the entities belonging to the actual
world, from our limited history and limited access to its constituent
facts. There is surely much about the actual world that we do not yet
know, that we may never know, and that we cannot infer from experi-
ence of the tiny corner of the universe that falls under even our most
instrumentally enhanced survey, or from the infancy of our logic, math-
ematics, natural science and philosophy. We do not know whether
physical, abstract and intentional kinds of entities exhaust the main
categories of existents in the actual world, or whether there are other
kinds of entities as different as these three categories of abstract entities
are different from physical entities, and as different as intentional
entities are different again from both physical and abstract entities, that
have yet to be discovered and assimilated into our conceptual schemes
in an appropriately enlarged scientific ontology.
Ontology is scientific in so far as it remains open to such possibili-
ties in theory or in principle. We may not have any informative way to
represent potential ontic discoveries even within the lavish resources
of the imagination, but which at this stage of human enquiry we have
as yet no good reason to exclude. If the future course of mathematics,
science and philosophy is even partially uncharted, then so to the
same degree and for the same reason is the future course of applied
scientific ontology. We do not know what remains to be known and
how scientific and philosophical ontology might need to develop.
That is part of the excitement, provided that the basic framework of
our integrated pure philosophical and applied scientific ontology is
sufficiently flexible to accommodate novelties that are not already
covered by the ontology at any penultimate stage of its ongoing
development.
It would be incompatible with the characteristic features of scien-
tific method to suppose that the work of ontology can ever be the final
280 ONTOLOGY
statement about the absolute meaning and nature of existence. At
least these matters must remain open-ended while the project of
empirical science and philosophical reflection is incomplete, and
while there are still outstanding unanswered questions of science. If
the project of ontology continues indefinitely, we can nevertheless
hope that we have now correctly sketched the method, scope and
limits of pure philosophical ontology with enough care so as to
provide an adequate analysis of the concept of being and the outline
for a corresponding theory of applied scientific ontology. To the
extent that we have succeeded, we will have advanced a structure for
the ongoing work of applied scientific ontology that offers a system-
atic way of approaching the most difficult outstanding questions of
existence.
We grasp the concept of being only when we have satisfactorily
answered the question why there is something rather than nothing
and why there is only one logically contingent actual world. If we
arrive at an understanding of the nature of being, of what it means for
something to exist, then we can begin to make sense and judge the
truth of the proposition that a certain choice of putative entities exist
or do not exist. We can then, but only then, take the first steps
towards an applied scientific ontology, in which we decide whether to
include or exclude any putative entity from a preferred existence do-
main. It is only at this stage of ontological enquiry that we can mean-
ingfully enquire whether or not there are good reasons to approve the
existence of the usual ontological suspects, standardly beginning, as in
preceding chapters, with physical entities of various types, and pro-
ceeding to abstract objects, minds and persons, God, language, art
and cultural artefacts. Whether or not this is the standard sequence of
topics for applied scientific ontology, it is by no means universal. It is
open to alternative applied ontologies to begin with the ontic status of
God, and proceed to universals, and only then take up the ontology of
physical entities; or to begin with mind and then introduce good
reasons for supporting or rejecting a given category of numbers, sets
or propositions; or to begin with propositions and proceed from
thence to other applied ontological categories. At that point, pure
logic no longer plays a leading role as it does in pure philosophical
ontology in justifying a preferred existence domain as a contribution
to applied scientific ontology. Applied scientific ontology, unlike the
conceptual analysis of the meaning of being in pure philosophical
ontology, must inevitably remain a work in progress in scientific
philosophy.
Notes
Part I: Pure Philosophical Ontology
Chapter 1: What it is to be (on Heidegger)
1. The distinction between the verb of being and its cognates in existence and predi-
cation senses is essential. There is a grammatical difference of philosophical inter-
est in saying that an object is or is not (simpliciter, full stop), as opposed to saying
that an object is or is not red or mortal or fascinating, in attribution of a property.
The ambiguity in the two senses of “is” or “to be” is illustrated by W. V. O. Quine’s
syntactical criterion of ontological commitment, discussed at length in Chapter 6.
Quine, “On What There Is”, in From a Logical Point of View, 2nd edn, rev. (New
York: Harper & Row, 1963a), pp. 6–7, 15–16, maintains that “To be is to be the
value of a [quantifier-bound] variable.” Here the first occurrence of the verb phrase
“to be” is clearly intended in the existence sense, and the second occurrence in the
complete context, “to be the value of a variable”, is obviously predicational. If the
distinction between the existence and predication senses of being is not observed,
then Quine’s criterion, whatever its other merits or defects, is viciously circular,
saying in effect that to exist is to exist. Verbs of being in the predication sense can
also be used to predicate the property of existing or not existing to an object, as
when we say that the Taj Mahal is or has the property of being a real existent thing,
or that the flying horse is not existent, or does not have the property of being an
existent entity. Recognizing the difference between the existence and predication
senses of being is the first step toward understanding their logical interrelations in
pure philosophical ontology. A fundamental difference in ontology is marked by
whether a theory tries to explain existence in terms of predication (intensional), or
predication in terms of existence (extensional). See note 3.
2. Aristotle, Metaphysics 1003a32–1005a18. F. Brentano, On the Several Senses of
Being in Aristotle, R. George (ed. and trans.) (Berkeley, CA: University of Califor-
nia Press, 1975) (translation of Brentano’s 1862 dissertation, Von der
mannigfachen Bedeutung des Seienden nach Aristoteles). In 1907 Heidegger
received a copy of Brentano’s work from a family friend, Conrad Gröber. The book
made an enormous impression on Heidegger’s ontology, prompting him in the
preface to W. J. Richardson (ed.), Heidegger: Through Phenomenology to Thought
(The Hague: Martinus Nijhoff, 1963) to write of Brentano’s study that it had posed
“the question that determined the way of my thought: what is the pervasive,
simple, unified determination of Being that permeates all of its multiple
282 ONTOLOGY
meanings?” (p. x). He adds, “The first philosophical text through which I worked
my way again and again from 1907 on, was Franz Brentano’s Von der
mannigfachen Bedeutung des Seienden nach Aristotles” (p. xi). See J. Owens, The
Doctrine of Being in the Aristotelian Metaphysics: A Study in the Greek Background
of Medieval Thought, 3rd edn, rev. (Toronto: Pontificial Institute of Mediaeval
Studies, 1978) and F. Volpi, “Heideggers Verhaltnis zu Brentanos Aristoteles-Inter-
pretation: Die Frage nach dem Sein des Seienden”, Zeitschrift für philosophische
Forschung 32.
3. The distinction between intensional and extensional linguistic or logical contexts
and theories is characterized in different ways and identified by a variety of criteria.
For present purposes, a context or theory is said to be extensional if it defines prop-
erties and interprets predicates and the truth-value of predications in terms of the
existent entities that belong to the extension of a predicate as the set of existent
entities possessing the properties represented by a predicate. An intensional con-
text or theory, in contrast, negatively speaking, is one that is not extensional; more
positively defined, it is a context or theory that defines objects independently of
their ontic status and interprets names and descriptors and the truth-value of
predications in terms of particular property combinations. The distinction between
intension and extension as we have presented it further entails the applicability of
the more familiar criterion by which intensional contexts and theories are distin-
guished from extensional ones on the basis of intersubstitution failures salva
veritate of coreferential terms and logically equivalent sentences, restrictions on
truth-preserving quantifying-in, existential generalization and related qualifica-
tions of intensional contexts.
4. Semantic extensionalism implies that a property can be truly predicated of an object
only if the object exists. Against extensionalist presuppositions, we argue that we
cannot make sense of the nonexistence of specific nonexistent objects except in
terms of their possessing certain combinations of jointly uninstantiated properties.
If semantic extensionalism is true, then if God does not exist, we cannot say that our
concept of God is the concept of something omnipotent, omniscient and perfectly
benevolent, or of an at least imagined object to whom those properties are truly
predicated, independently of God’s ontic status as existent or nonexistent. This
makes it fallacious to infer that God exists from the proposition that God is or has
the property of being omnipotent, or any other property correctly attributed to God
or the concept of God. We need a certain amount of logical distance between the
predication of constitutive properties and the existence or nonexistence of the ob-
jects to which properties are predicated. The reason why God does not exist, accord-
ing to atheists persuaded by the problem of natural evil, for example, is that God or
the concept of God is inconsistently defined as being omnipotent, omniscient, per-
fectly benevolent and the creator of a vastly imperfect world. If God as traditionally
understood did not truly have these properties, then there would be no basis for such
an atheist correctly or incorrectly to question God’s existence. The ontic neutrality
of constitutive property predications for the same reason is crucial to understand-
ing the logical failure of Anselm’s so-called ontological argument for the existence
of God. See Chapter 11 and Chapter 11, note 2.
5. It appears a superficial distinction whether we ostensibly refer to Pegasus by name
or to the flying horse by definite description. It should therefore not matter
whether we try to attribute the properties of flying and being a horse to Pegasus or
to the flying horse, since Pegasus is just a name for the flying horse. According to
Bertrand Russell’s extensionalist theory of definite descriptions in his 1905 essay
“On Denoting”, Mind 14, the predication of a property to an object designated by
a proper name is analysable as a definite description with three clauses, including
an existence assertion, a uniqueness assertion and a predication of the property to
NOTES 283
the uniquely definitely described existing thing. Symbolically, the analysis of a
definite description, “The F is or has property G”, on Russell’s theory, is formu-
lated as: [ ]   ÷ ¯ r V ÷ · r
 
G xFx x Fx y Fy x y Gx . Russell interprets proper
names as disguised definite descriptions, so that to say that Pegasus is a flying horse
is just as false as to say that the flying horse is a flying horse, both of which
predications fail to satisfy Russell’s extensionalist existence condition. If we think
of logically possible predication objects combinatorially in terms of a distinguishing
combination of constitutive properties, then we properly leave open the question
of their contingent existence or nonexistence when we assign truth-values to the
predications of properties to objects. The ontic neutrality of intensionally defined
objects further avoids the long-standing problem about the concept of non-being
considered in Plato’s dialogues the Sophist and Parmenides. We do not need to say
that Pegasus paradoxically must exist in order to be the predication subject of the
true proposition that Pegasus does not exist, if the logical objects of pure philo-
sophical logic and ontology are intensionally rather than extensionally interpreted.
A related approach to Plato’s problems featuring a complex choice of analyses of
the concept of negation is offered by F. J. Pelletier, Parmenides, Plato, and the
Semantics of Not-Being (Chicago, IL: University of Chicago Press, 1990) and
“Plato on Not-Being: Some Interpretations of the ‘Symploki Eidon’ (259e) and
Their Relation to Parmenides’ Problem”, Midwest Studies in Philosophy 8 (1983).
6. Some medieval metaphysicians distinguish between concrete physical spatio-
temporal existence and abstract non-physical non-spatiotemporal subsistence as
distinct modes of being. A special third category of spiritual being is also added in
theological and philosophical contexts to account for souls, angels and even the
being of God as neither physical nor abstract. The scholastic distinction between
existence and subsistence is adopted by Russell, and appears in various guises in
recent and contemporary logical and metaphysical systems. We shall not observe
any form of the existence–subsistence distinction, but collapse the concepts into
one by equating existence with being and allowing the two terms to be used
synonymously, eliminating references to subsistence altogether. We continue to
distinguish between concrete physical or spatiotemporal being or existence and
abstract non-physical non-spatiotemporal being or existence, as categories of a
preferred applied scientific ontology.
7. M. Heidegger, Being and Time: A Translation of Sein und Zeit, J. Stambaugh
(trans.) (Albany, NY: State University of New York Press, 1996), p. 9.
8. Ibid., p. 31.
9. Ibid., p. 34.
10. Before 1927 Heidegger underwent a dramatic swing away from Husserlian phe-
nomenology, known to Heidegger scholars as die Kehre (literally, the “turn”).
Husserl’s phenomenology nevertheless underlies even Heidegger’s later ontology,
which Heidegger in obvious ways transforms for his own purposes in articulating
the existentialist principles of Da-Sein. Although Heidegger is not explicit about
this aspect of his methodology, he seems to rely on the fact that Husserl’s epoché,
and especially transcendental epoché, is a priori in its bracketing or suspension of
any belief about the ontic status of objects presented to thought for internal struc-
tural phenomenological analysis. E. Husserl, Ideas: General Introduction to Pure
Phenomenology, W. R. Boyce Gibson (trans.) (New York: Collier Books, 1962);
Logische Untersuchungen, 2nd edn, G. Patzig (ed.) (Göttingen: Vandenhoeck &
Ruprecht, 1966); Cartesian Meditations: An Introduction to Phenomenology, D.
Cairns (trans.) (The Hague: Martinus Nijhoff, 1977). See C. F. Gethmann, Dasein:
Erkennen und Handeln: Heidegger im phänomenologischen Kontext (Berlin:
Walter de Gruyter, 1993), J. R. Mensch, The Question of Being in Husserl’s Logical
Investigations (The Hague and Boston: Kluwer, 1981), D. Moran, “Heidegger’s
284 ONTOLOGY
Critique of Husserl’s and Brentano’s Accounts of Intentionality”, Inquiry 43
(2000), R. J. Dostal, “Time and Phenomenology in Husserl and Heidegger”, in The
Cambridge Companion to Heidegger, C. B. Guignon (ed.) (Cambridge: Cambridge
University Press, 1993) and T. Kisiel, “On the Dimensions of a Phenomenology of
Science in Husserl and the Young Dr. Heidegger”, Journal of the British Society for
Phenomenology 4 (1973).
11. Heidegger, Being and Time, especially, pp. 132–7, 141–86, on disclosedness
(Erschlossenheit), and pp. 121–7, 171–230 and passim, on care (Sorge).
12. M. Merleau-Ponty, The Phenomenology of Perception, C. Smith (trans.) (New York:
The Humanities Press, 1962), especially pp. 67–199, on the concept of the lived-
body. See D. W. Smith, “Bodily Versus Cognitive Intentionality”, Noûs 22 (1988).
13. The topic is featured in many commentaries on Heidegger’s Being and Time. An
insightful comparison is offered by J. Young, “Schopenhauer, Heidegger, Art, and
the Will”, in Schopenhauer, Philosophy, and the Arts, D. Jacquette (ed.)
(Cambridge: Cambridge University Press, 1996).
14. Heidegger, Being and Time, p. 6.
15. Ibid.
16. Ibid.
17. Ibid., p. 290.
18. Ibid., pp. 290–91. See also M. Heidegger, Existence and Being (South Bend:
Gateway Editions, 1976b), pp. 11–116.
19. R. Descartes, Meditations on First Philosophy (1641), in The Philosophical Works
of Descartes [2 volumes], E. S. Haldane and G. R. T Ross (trans.) (Cambridge:
Cambridge University Press, 1975), dedicatory epistle:
And although it is utterly true that God’s existence is to be believed in
because it is taught in the Holy Scriptures, and, on the other hand, that the
Holy Scriptures are to be believed because they have God as their source
(because, since faith is a gift from God, the very same one who gives the
grace that is necessary for believing the rest, can also give us grace to
believe that he exists); nonetheless, this cannot be proposed to unbelievers
because they would judge it to be a circle. (p. 1)
20. Heidegger, Being and Time, p. 291.
21. Ibid.
22. See H. Philipse, Heidegger’s Philosophy of Being: A Critical Interpretation
(Princeton, NJ: Princeton University Press, 1998). For a more sympathetic exposi-
tion, compare J. Taminiaux, Heidegger and the Project of Fundamental Ontology,
M. Gendre (trans. and ed.) (Albany, NY: State University of New York Press, 1991)
and D. C. Hoy, “Heidegger and the Hermeneutic Turn”, in The Cambridge Com-
panion to Heidegger, C. B. Guignon (ed.) (Cambridge: Cambridge University Press,
1993), especially pp. 185–9.
23. Heidegger, Being and Time, p. 6.
24. Ibid.
25. Ibid.
26. Ibid., p. 12.
27. Ibid., p. 108.
28. Heidegger, Being and Time, especially, pp. 113–30, 161–4, 237–8, 263–4, 270–72,
280–83, on the concept of Mitda-sein.
29. Ibid., p. 341.
30. Ibid., p. 342.
Chapter 2: Combinatorial ontology
1. See G. W. Leibniz, De Arte Combinatoria, in Sämtliche Schriften und Briefe, series
NOTES 285
VI [16 volumes], volume 1 (Berlin: Akademi-Verlag) (originally published in 1666
as Dissertatio), L. Wittgenstein, Tractatus Logico-Philosophicus, C. K. Ogden (ed.)
(London: Routledge & Kegan Paul, 1922) and A. Blass, “Infinitary Combinatorics
and Modal Logic”, Journal of Symbolic Logic 55 (1990).
2. Logic is a more appropriate a priori method for ontology than phenomenology.
Whereas logic abstracts its normative principles of reasoning from specifically
human thinking, Husserl’s and certainly Heidegger’s existentialist phenomenology
makes the thinker an essential part of phenomenological analysis even when the
existence of objects thought about are bracketed in an ontically neutral epoché. In
The Metaphysical Foundations of Logic, M. Heim (trans.) (Bloomington, IN:
Indiana University Press, 1984), Heidegger has things precisely reversed from this
perspective, construing logic and even the concept of truth as a consequence rather
than presupposition of the phenomenology of judgement.
3. An important difference between the combinatorial theory of logically possible
objects and properties and Wittgenstein’s logic in Tractatus Logico-Philosophicus is
that in the Tractatus simple objects exist in every logically possible world.
Wittgenstein does not refer to logically possible worlds as such, but maintains that
“Objects form the substance of the world. Therefore they cannot be compound”
(§2.021). By considering simple objects as the world’s substance, Wittgenstein
implies that the same objects can be combined into any possible configuration of
facts, and therefore into any logically possible world. The objects of combinatorial
ontology need not be simple nor, except in the case of abstract objects, if there are
any, must they exist in every logically possible world; they are instead logically
possible predication subjects, only some of which actually exist only in the actual
world.
4. The ontological priority of objects is defended in another way by P. F. Strawson,
Individuals: An Essay in Descriptive Metaphysics (Garden City, NY: Doubleday,
1963), pp. 136–219. A similar but more elaborate proposal featuring actual events
as the basic objects of ontology is advocated by A. N. Whitehead, Process and Real-
ity: An Essay in Cosmology (New York: The Free Press, 1929). See J. W. Lango,
Whitehead’s Ontology (Albany, NY: State University of New York Press, 1972).
From the standpoint of combinatorial pure philosophical ontology, both Whitehe-
ad’s and Strawson’s projects appear to substitute applied ontology in the form of a
list or descriptive inventory of the kinds of things that exist, along with an account
of their explanatory usefulness in metaphysics, and are otherwise exercises in
applied ontology that do not even attempt to answer fundamental questions about
the concept of being.
5. Aristotle, Metaphysics 1005b22-34, 1006b19, 1007a20, 1008a29-b2 . A. Code,
“Aristotle’s Investigation of a Basic Logical Principle: Which Science Investigates
the Principle of Non-Contradiction?”, Canadian Journal of Philosophy 10 (supple-
ment) (1986). I. Kant, Critique of Pure Reason, N. Kemp Smith (trans.) (New York:
St Martin’s Press, 1965), A786/B814–A789/B817, A737/B765. The method of
argument in both Aristotle and Kant is related to but more specialized than that
of indirect proof or reductio ad absurdum. A reductio argument proves the nega-
tion of any hypothesis that together with other assumptions leads to a contradic-
tion or literally reduces the hypothesis to an absurdity. Aristotle’s defence of non-
contradiction and Kant’s method of transcendental reasoning by contrast uphold
the truth of an assumption when any attempt to question or cast doubt on the
assumption presupposes that the assumption is true.
6. The central thesis of combinatorial ontology is that objects as logically possible
predication subjects are constituted by combinations of properties independently
of their ontic status. These in turn can be further combined with properties in
logically possible predications expressed by propositions representing logically
286 ONTOLOGY
possible states of affairs or object–property combinations. This raises questions
about just what kinds of things count as objects. The answer is that we can have any
combination of properties constituting objects, not all of which belong to any logi-
cally possible world. If the semantics is expanded to include logically impossible
worlds, then there is no need to observe the consistency restriction on combina-
tions of properties by which objects are constituted for purposes of predication
with other properties. Combinatorial pure philosophical ontology, as opposed to a
general semantics, requires only logically possible worlds involving the logically
possible properties of logically possible objects. We obtain an object for pure ontol-
ogy in the combination [golden, mountain], which we can name or represent by
means of definite descriptions as “a” or “the golden mountain”, and to which we
can consider predications of other properties in true or false propositions, some of
which will be logically or analytically true or false, and others contingently true or
false. We can say, for example, as a logical and analytic truth, that the golden moun-
tain is golden, Ga or G[golden, mountain] or golden[golden, mountain], or even
Gix[Gx r Mx]. We do the same for impossible combinations like [golden, non-
golden] or [carnivorous, vegetarian], and for predications colloquially expressed as
“Every human is a prime number”, “Every prime number is divisible by itself, 1,
and at least one other number”, “Green ideas sleep furiously” and the like.
Predicationally inconsistent impossible objects have no place in an ontology under-
stood as a formal theory of being, since, by virtue of their internally metaphysically
impossible property combinations, no such things can possibly exist.
7. A concise explanation of Lindenbaum’s Lemma is given by E. Mendelson, Intro-
duction to Mathematical Logic (New York: D. Van Nostrand, 1964), pp. 64–5. See
note 17.
8. The intensional logic presented here as a contribution to pure philosophical ontol-
ogy involving logically possible objects is a fragment of a complete intensional
theory of meaning. A complete intensional semantics is not limited to logically
possible objects, states of affairs and worlds, but needs also to include impossible
intended objects. Any predication subject is an object, but not every predication
subject is a logically possible object relevant to the formalization of a pure philo-
sophical ontology. An obvious example is ix[Fx r
-
Fx]. Impossible objects are
equivalently combinatorially definable by means of abbreviations, taking “F1” as
the property of being an animal other than a horse and “F2” as the property of
being a horse, it is logically possible to combine the properties in the logically and
analytically impossible object, [F1, F2]. Such logically nonexistent objects again are
indispensable in a complete semantics of thought and discourse, but fall outside the
scope of ontology. For this reason, it is sometimes said that an intensional semantics
requires an extraontology of intended objects that are not even logically possible, as
well as an ontology of existent or at least logically possible objects. On the seman-
tics for logically impossible worlds, see G. Priest’s guest-edited issue of Notre Dame
Journal of Formal Logic 38 (1997), “Impossible Worlds”, including contributions
by E. D. Mares, “Who’s Afraid of Impossible Worlds?”, D. Nolan, “Impossible
Worlds: A Modest Approach”, D. A. Van der Laan, “The Ontology of Impossible
Worlds” and J. Hintikka, “Impossible Possible Worlds”. See also the distinction
between “inconsistent” and “impossible” worlds in N. Rescher and R. Brandom,
The Logic of Inconsistency: A Study in Non-Standard Possible-World Semantics and
Ontology (Totowa: Rowman and Littlefield, 1979).
9. C. I. Lewis, A Survey of Symbolic Logic (Berkeley, CA: University of California
Press, 1918); “Implication and the Algebra of Logic”, Mind 21 (1912); “Interesting
Theorems in Symbolic Logic”, Journal of Philosophy 10 (1913); “The Matrix Alge-
bra for Implication”, Journal of Philosophy 11 (1914); “Strict Implication: An
Emendation”, Journal of Philosophy 17 (1920). C. I. Lewis and C. H. Langford,
NOTES 287
Symbolic Logic, 2nd edn (New York: Dover, 1959).
10. S. A. Kripke, “Semantical Considerations on Modal Logics”, Acta Philosophica
Fennica 16 (1963a); “Semantical Analysis of Modal Logic I: Normal Modal
Propositional Calculi”, Zeitschrift für mathematische Logik und Grundlagen der
Mathematic 9 (1963b). J. Hintikka, ‘”The Modes of Modality”, Acta Philosophica
Fennica 16 (1963).
11. See D. K. Lewis, Counterfactuals (Oxford: Basil Blackwell, 1973). Some develop-
ments of model set-theoretical semantics for modal logic do not refer to the actual
world as such, but make passing reference to the fact that the actual world is to be
included as one among all logically possible worlds, and consider only generalized
accessibility relations relative to any arbitrary world o. An example is B. F. Chellas,
in his Modal Logic: An Introduction (Cambridge: Cambridge University Press,
1980), who does not define the concept of a logically possible world but treats it as
primitive or intuitive. A generalized semantics of the sort Chellas considers must be
supplemented with a method of designating the actual world for applications such
as the interpretation of counterfactual propositions, in which the facts of the actual
world are contrasted with propositions that are supposed to be true in alternative
logically possible worlds via some specification of world-to-world modal accessibil-
ity relations.
12. S. A. Kripke, Naming and Necessity (Cambridge, MA: Harvard University Press,
1980):
A possible world isn’t a distant country that we are coming across, or
viewing through a telescope. Generally speaking, another possible world is
too far away. Even if we travel faster than light, we won’t get to it. A possi-
ble world is given by the descriptive conditions we associate with it . . .
“Possible worlds” are stipulated, not discovered by powerful telescopes.
There is no reason why we cannot stipulate that, in talking about what
would have happened to Nixon in a certain counterfactual situation, we are
talking about what would have happened to him. (p. 44)
See N. Salmon, “Trans-world Identification and Stipulation”, Philosophical Studies
84 (1996).
13. G. Forbes, The Metaphysics of Modality (Oxford: Clarendon Press, 1985):
The discussion of the previous section should have imparted a general
picture of what model theory for quantified S5 is going to look like. As in
the sentential case, there will be a set of possible worlds, but in addition,
each world will be assigned a set of objects, the things which exist at that
world. (p. 28)
See also G. Forbes, Languages of Possibility: An Essay in Philosophical Logic
(Oxford: Basil Blackwell, 1989), and D. K. Lewis, On the Plurality of Worlds (Ox-
ford: Basil Blackwell, 1986). Additional references on the realism–actualism con-
troversy in the metaphysics of modal logic notably include C. S. Chihara, The
Worlds of Possibility: Modal Realism and the Semantics of Modal Logic (Oxford:
Clarendon Press, 1998), see below, note 20; R. Stalnaker, “On Considering a
Possible World as Actual I”, Proceedings of the Aristotelian Society, Supplement 75
(2001); M. Bergmann, “A New Argument from Actualism to Serious Actualism”,
Noûs 30 (1996); P. Bricker, “‘Isolation and Unification: The Realist Analysis of
Possible Worlds”, Philosophical Studies 84 (1996); S. Bringsjord, “Are There Set
Theoretic Possible Worlds?”, Analysis 45 (1985); J. Divers, “Modal Fictionalism
Cannot Deliver Possible Worlds Semantics”, Analysis 55 (1995); P. Grim, “On Sets
and Worlds: A Reply to Menzel”, Analysis 46 (1986); B. Hale, “Modal Fictionalism
– A Simple Dilemma”, Analysis 55 (1995); A. Hazen, “Expressive Incompleteness
in Modal Logic”, Journal of Philosophical Logic 5 (1976) and “Actualism Again”,
Philosophical Studies 84 (1996); T. Jager, “An Actualist Semantics for Quantified
288 ONTOLOGY
Modal Logic”, Notre Dame Journal of Formal Logic 23 (1982); M. Jubien,
“Actualism and Iterated Modalities”, Philosophical Studies 84 (1996); J. Kim,
“Possible Worlds and Armstrong’s Combinatorialism”, Canadian Journal of
Philosophy 16 (1986); A. McMichael, “A New Actualist Modal Semantics”,
Journal of Philosophical Logic 12 (1983a) and “A Problem for Actualism About
Possible Worlds”, Philosophical Review 92 (1983b); C. Menzel, “On Set Theoretic
Possible Worlds”, Analysis 46 (1986) and “Actualism, Ontological Commitment,
and Possible Worlds Semantics”, Synthese 85 (1990); A. Plantinga, “Actualism and
Possible Worlds”, in The Possible and the Actual, M. J. Loux (ed.) (Ithaca, NY:
Cornell University Press, 1979); G. Ray, “Ontology-Free Modal Semantics”, Jour-
nal of Philosophical Logic 25 (1996); P. Van Inwagen, “Two Concepts of Possible
Worlds”, Midwest Studies in Philosophy 11 (1986); and S. Yablo, “How in the
World?”, Philosophical Topics 24 (1996).
14. Modal actualist combinatorial possible worlds semantics does not preclude infor-
mal reference to the existence of an object or state of affairs in or at a non-actual
world. Such language is not to be taken literally even in the case of conventional
model set-theoretical semantics. When, for convenience, we say that Sherlock
Holmes exists in another world, we mean only that a non-actually merely logically
possible world is defined in part by means of constitutive predications of properties
to a non-actual merely logically possible object stipulatively designated as Sherlock
Holmes. See G. Rosen, “Modal Fictionalism”, Mind 99 (1990), “A Problem for
Fictionalism About Possible Worlds”, Analysis 53 (1993), and “Modal Fictionalism
Fixed”, Analysis 55 (1995).
15. Conventional modal realist model set-theoretical semantics disconcertingly tries to
hold at the same time that logically possible worlds as maximally consistent propo-
sition sets exist, and that objects and states of affairs in some sense exist in or at
even non-actual logically possible worlds, but that only the actual world and the
objects and states of affairs it contains actually exist. To speak of actual existence
and of a thing’s actually existing seems unobjectionable for the sake of redundant
emphasis, but when actual existence is distinguished from existence or existence in
or at a non-actual merely logically possible world, a sound basis for the distinction
is required, which conventional modal realist model set-theoretical semantics, with
its concept of a logically possible world as a maximally consistent proposition set,
does not provide. The modal semantics considered in pure philosophical ontology
is itself pure rather than applied. The modal actualism of the combinatorial analysis
of alethic modality already has built into it a principled distinction between the one
and only existent or actual maximally consistent world and all other non-actual or
fictional submaximally consistent merely logically possible worlds as a feature of its
pure semantics. The modal realism of conventional model set-theoretical modal
semantics by contrast permits it to distinguish and identify the actual world only in
its applications. The characterization of the exact content and condition of the
actual world remains a practical task for applied rather than pure combinatorial
modal semantics, and, of course, for history and the descriptive natural sciences.
16. Even if a correct or most satisfactory semantics for modal logic turns out to be some
version of conventional model set-theoretical semantics incorporating the standard
concept of a logically possible world as a maximally consistent proposition set, we
cannot avail ourselves of the fact that logically possible worlds exist as abstract
entities on such a conception while engaged in trying to address the question of
being as a problem of pure philosophical ontology. See M. McKeon, “Logical Truth
in Modal Logic”, Pacific Philosophical Quarterly 77 (1996).
17. Lindenbaum’s Lemma entails that if I is a syntactically consistent proposition set,
then I is a subset of some maximally consistent proposition set that is an extension
of I. If proposition p is actually true, then any world in which ¬p is true must be
NOTES 289
submaximal, according to the combinatorial account of non-actual merely logically
possible worlds. This fact nevertheless does not contradict Lindenbaum’s Lemma.
The combinatorial analysis does not identify or equate logically possible worlds
with proposition sets, whether they are maximally or submaximally consistent.
What is true of proposition sets as an implication of Lindenbaum’s Lemma does not
therefore translate into any consequences for the modal actualist combinatorial
concept of a logically possible world as a logically possible states-of-affairs combi-
nation.
18. Is it true, as a combinatorial modal actualist semantics entails, that all non-actual
merely logically possible worlds are submaximal? Can we not imagine a logically
possible world that is just like the actual world in every respect except for the exist-
ence or nonexistence of an elementary particle in a remote corner of intergalactic
space that is not in causal interaction with any other part of the universe? Such a
particle exists or does not exist, but in either case the scenario appears to project a
non-actual merely logically possible world that by virtue of its method of description,
beginning with the maximally consistent actual world and considering only one
small change, is maximally consistent in the constitutive properties of all its
constituent objects and states of affairs. It is essential to the counterexample that the
logically possible world in question involves a physical and hence logically
contingent entity that is causally isolated in every way from every other event in the
universe, since otherwise we would not be able to comprehend all of the ramifica-
tions of introducing such a change without taking account of the untold alterations
that would cascade throughout that world. It need not be problematic to imagine a
causally inefficacious physical transformation within the actual world as a mere
logical possibility. Even without causal modifications, however, the addition to or
deletion from a complete world of one such particle or physical entity of any size
introduces unlimitedly many predication gaps in the stipulative projection of a non-
actual world. Any such world is sure to be incomplete with respect to innumerable
spatiotemporal relations between the imagined particle and every other physical
entity in the universe in what is consequently bound to be at best a submaximal speci-
fication of the non-actual world’s states of affairs. The same is true if we think of
spacetime as involving a branching future with no predetermined course, in which
only one pathway is ultimately realized. The way the world turns out to be is describ-
able as the actual occurrence of one of the many branching paths open to it any point,
in which all as yet unrealized potential routes are projected when and in so far as they
are only considered as submaximal logical possibilities, including whatever particu-
lar path later turns out to be actual – which is to say, on the combinatorial modal
actualist analysis, whatever path turns out to be maximally consistent.
19. The idea of a logically possible world as a maximal structure of facts or proposi-
tions is clearly stated in Forbes, The Metaphysics of Modality:
A possible world is a complete way things might have been – a total alter-
native history . . . In terms of our model theory, the requirement that
worlds be complete is reflected in the constraint that every sentence letter
occurring in the argument in question be assigned one or other truth value
at each world. (p. 8)
This intuitive statement of the semantic concept of a logically possible world is
equivalent to the conventional modal realist definition of a world as a maximally
consistent proposition set. Significantly, Forbes adds, “We shall see in §4 of this
chapter that we can get by without this sort of completeness, but that we pay a price
in terms of simplicity” (ibid.).
20. In The Worlds of Possibility, Chihara argues that a Cantorian cardinality paradox
afflicts A. Plantinga’s set-theoretical principles of modal semantics in The Nature of
Necessity (Oxford: Oxford University Press, 1974). Chihara identifies the follow-
290 ONTOLOGY
ing assumptions in Plantinga’s modal ontology:
[1] States of affairs exist. [2] Every state of affairs S has a complement S´. [3]
If S is a state of affairs, then necessarily either S or S´ obtains. [4] Given any
possible state of affairs S, there exists a set whose members are all those
possible states of affairs whose members are all those possible states of
affairs that include S. [5] Given any set µ of states of affairs, the conjunction
of that set, all the members of µ having obtained, exists. (p. 125)
Chihara infers the existence of at least one logically possible world by building up
a set µ, adding either S or the complement of S, S´, for every S, and defining D as the
state of affairs of all the states of affairs in µ having obtained. (This is a version of
the Lindenbaum maximal consistency recursion; see above, notes 7 and 17.) Set D
thereby satisfies the conventional model set-theoretical definition of a logically
possible world, which Plantinga also accepts, the existence of which, by Plantinga’s
principles, is set-theoretically guaranteed. Chihara then deduces a Cantorian para-
dox:
As shown above, we can conclude from Plantinga’s principles that there is
a set o whose elements are all the possible states of affairs that obtain.
Then, according to Cantor’s Theorem, the power set of o, 2
o
, has
cardinality greater than the cardinality of o. Hence, there cannot be a one-
one correspondence between 2
o
and any subset of o. But, as will be shown
below, there is. (p. 126)
The proposed combinatorial analysis of alethic modality avoids Chihara’s
Cantorian paradox by detaching the concept of a logically possible world from that
of a maximally consistent proposition or states of affairs set like D. Chihara’s para-
dox refutes conventional model set-theoretical concepts of a logically possible
world, like Plantinga’s. Importantly, the combinatorial model does not accept
Plantinga’s principle [2], that all states of affairs exist, since not all states of affairs
are maximally consistent. Nor does Chihara’s proof of the existence of at least one
logically possible world on Plantinga’s realist assumptions go through in a combi-
natorial actualist modal ontology and semantics. At most, Chihara establishes a
result that is limited in immediate relevance to set theory in the abstract, including
conventional set-theoretical models of logical possibility. In proving the existence
of set D, Chihara establishes the existence of at least one maximally consistent
states-of-affairs set. From a combinatorial modal actualist perspective, however, he
does not thereby prove the existence of a logically possible world. The only
logically possible world recognized as existent in actualist combinatorial modal
semantics is the actual world, and it is not an abstract set but a maximally consistent
states-of-affairs combination. Chihara, moreover, does not explain exactly what he
means by a state of affairs “obtaining”. If by this he means simply existing, then
combinatorial ontology in any case cannot rely on Chihara’s applied ontological
assumptions about the ontic status of abstract entities such as states of affairs and
sets of states of affairs, including the state of affairs in which other states of affairs
obtain. Assumptions about the ontic status of sets and states of affairs cannot be
introduced without falling into Heidegger’s circle while the question of being in
pure philosophical ontology remains unanswered, and so cannot be appealed to in
trying to prove either the existence of at least one logically possible world or of the
actual world as the only existent logically possible world. Cantor’s diagonalization
proof of the generalized power set principle to which Chihara refers appears in G.
Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, P. E.
B. Jourdain (trans.) (New York: Dover, 1952).
NOTES 291
Chapter 3: Why there is something rather than nothing
1. G. W. Leibniz, “On the Ultimate Origination of Things”, in Leibniz: Philosophical
Writings, G. H. R. Parkinson (ed.), M. Morris and G. H. R. Parkinson (trans.)
(London: J. M. Dent and Sons 1973e), pp. 136–44.
2. Leibniz’s concept of an haecceity or individuating essence, together with his com-
mitment to the principle of the identity of indiscernibles, that x = y if x and y share
all their properties in common, poses difficulties for the common-sense view that
the very same objects in the actual world might have different properties in alterna-
tive non-actual merely logically possible worlds. The combined force of these pos-
itions in Leibniz threatens to collapse all logically possible worlds into the actual
world, and render all predications of properties to existent entities logically neces-
sary. Further implications of Leibniz’s logic and metaphysics appear to contradict
the logical contingency of facts about physical spatiotemporal entities and the
freedom of action and the will. Leibniz tries to solve the problem informally by
sketching a theory of counterparts belonging to alternative logically possible
worlds that by degrees are relatively similar in their characteristic properties to
actual entities, and in terms of which logical contingencies and freedom can be in-
terpreted. Leibniz, Discourse on Metaphysics; Correspondence with Arnauld, G. R.
Montgomery (trans.) (La Salle, IL: Open Court, 1902); “Necessary and Contin-
gent Truth”, “On Freedom”, “A Letter on Freedom” and “On the Principle of
Indiscernibles”, collected in Leibniz: Philosophical Writings. See G. H. R.
Parkinson, Logic and Reality in Leibniz’s Metaphysics (Oxford: Clarendon Press,
1965). A contemporary exposition of counterpart theory for symbolic modal logic
is offered by D. K. Lewis, Counterfactuals and “Counterpart Theory and Quanti-
fied Modal Logic”, Journal of Philosophy 65 (1968).
3. M. Heidegger, An Introduction to Metaphysics, R. Manheim (trans.) (Garden City,
NY: Doubleday, 1961), pp. 1–42. A very different probabilistic approach to this
fundamental question of ontology is proposed by R. Nozick, Philosophical Expla-
nations (Oxford: Clarendon Press, 1981), pp. 115–64. See also N. Fleming, “Why
is There Something Rather Than Nothing?”, Analysis 48 (1988), C. Mortensen,
“Explaining Existence”, Canadian Journal of Philosophy 16 (1986), N. L. Wilson,
“The Two Main Problems of Philosophy”, Dialogue 12 (1973), R. Sylvan, “Toward
an Improved Cosmo-Logical Synthesis”, Grazer Philosophische Studien 25–26
(1985–86) and D. Parfit, “The Puzzle of Reality: Why Does the Universe Exist?”,
Times Literary Supplement, 3 July (1992).
4. Heidegger formulates the fundamental question of metaphysics in slightly different
terms. He asks, “Why are there essents rather than nothing?” (An Introduction to
Metaphysics: p. 1). Heidegger’s own asterisk note indicates that “‘Essents’ =
‘existents,’ ‘things that art [sic]’” (ibid.). Presumably, his choice of a special termi-
nology is meant to highlight the distinctive interpretation and solution of the ques-
tion he proposes. His avenue back to the existential ontology of Da-sein takes the
following direction. He argues (pp. 19–20) that the question can and should elimi-
nate the qualification “rather than nothing” as inessential. He maintains that the
abbreviated question “Why are there essents?” is to be addressed in terms of the
question “How is it with being?”, by which he means to ask whether being has a
ground or is itself a ground, in a roughly Kantian transcendental sense. His answer
is that being is itself a ground, to be understood in terms of Being and Time’s
phenomenology of Da-sein, whereby the original question “Why are there
essents?”, or “Why are there essents rather than nothing?”, is answered by main-
taining that being requires no transcendental ground or further explanation, but is
rather the ground of every existent thing that might be considered, presupposed
even by the fundamental question of metaphysics. Thus, Heidegger writes:
292 ONTOLOGY
Out of the fundamental question of metaphysics, “Why are there essents
rather than nothing?” we have separated the preliminary question, “How
does it stand with being?” . . . Here the preliminary question is not by any
means outside of the main question; rather, it is the flame which burns as
it were in the asking of the fundamental question; it is the flaming center
of all questioning. That is to say: it is crucial for the first asking of the fun-
damental question that in asking its preliminary question we derive the
decisive fundamental attitude that is here essential. That is why we have
related the question of being to the destiny of Europe, where the destiny
of the earth is being decided – while our own historic being-there proves
to be the center of Europe itself. (pp. 34–6)
All this seems a bit deluded; despite Heidegger’s efforts (pp. 24–5) to placate
concerns that Da-sein, as he conceives it, is anthropocentric and even ego-centric,
and (pp. 35–6) that his approach historicizes metaphysics, Heidegger explicitly
subordinates the question of being and the fundamental question of metaphysics to
the historical situation of a particular collection of (European) thinkers (on the
brink of world war) asking and trying to answer these questions. The conclusion is
further evidence of Heidegger’s entanglement in the methodological circle by
which his ontology and ontic sciences are snared. In the previous paragraph,
Heidegger writes:
We ask the questions “How does it stand with being?” “What is the
meaning of being?” not in order to set up an ontology in the traditional
style, much less to criticize the past mistakes of ontology. We are
concerned with something totally different: to restore man’s historical
being-there – and that always includes our own future being-there in the
totality of the history allotted to us – to the domain of being, which it was
originally incumbent on man to open up for himself. All this, to be sure,
within the limits within which philosophy can accomplish anything.
(p. 34)
Thereafter Heidegger adds:
Our asking the fundamental question of metaphysics is historical because
it opens up the process of human being-there in its essential relations – i.e.
its relations to the essent as such and as a whole – opens it up to unasked
possibilities, futures, and at the same time binds it back to its past begin-
ning, so sharpening it and giving it weight in its present. In this question-
ing our being-there is summoned to its history in the full sense of the
word, called to history and to a decision in history. And this not after the
fact, in the sense that we draw ethical, ideological lessons from it. No, the
basic attitude of the questioning is in itself historical; it stands and
maintains itself in happening, inquiring out of happening for the sake of
happening. (pp. 36–7)
It is tempting, although probably inaccurate, while at the same time virtually
impossible to know Heidegger’s final intent in his treatment of the fundamental
question of metaphysics, to interpret his solution as holding that the question
answers itself, because being as Da-sein is presupposed by the fact of the question’s
being asked. We have by now come to expect the extent to which Heidegger is
prepared to try to make a virtue out of this type of circularity.
5. C. G. Hempel, “Science Unlimited”, Annals of the Japan Association for Philosophy
of Science 14 (1973), p. 200.
6. Dasein in the ordinary non-Heideggerean sense means simply literally “being-
there” or “there-being” in German. For philosophical purposes, it is adopted by
many non-Heideggerean philosophers to represent the metaphysical category of
actual existence or real presence. The concept of das Modalmoment of full-
NOTES 293
strength factuality and depotenzierte or watered-down being in the object theory
tradition is introduced by Meinong, Über Möglichkeit und Wahrscheinlichkeit:
Beiträge zur Gegenstandstheorie und Erkenntnistheorie, Gesamtausgabe, VI, p.
266. See also J. N. Findlay, Meinong’s Theory of Objects and Values (Aldershot:
Ashgate Publishing, 1995), pp. 77, 103–12. Plato in Sophist 259e5–6 discusses the
blending or interweaving of the Form of Being with other Forms.
7. The circularity problem in Descartes’s Cogito is usually attributed only or primarily
to his version of the principle in the Discourse on Method, where he offers what
appears to be an explicitly inferential formulation, Cogito, ergo sum, as opposed to
the Meditations on First Philosophy, where it is simply made a matter of entertain-
ing a thought and recognizing that one must exist in order to think, Cogito, sum.
The difficulty is that the inflected Latin ending in the single word “Cogito” already
commits the expression to the proposition that it is specifially an I or ego, self, soul,
subject or first-person thinker that thinks, rather than, say, an impersonal force or
non-subjective impersonal occurrence or emanation of thought.
Chapter 4: Why there is only one logically contingent actual
world
1. Leibniz, “On the Ultimate Origination of Things” and Discourse on Metaphysics.
See G. M. Ross, Leibniz (Oxford: Oxford University Press, 1984), pp. 57–60.
2. See Russell’s common-sense refutation of “The First-cause Argument” in Why I Am
Not a Christian and Other Essays on Related Subjects, P. Edwards (ed.) (New York:
Simon and Schuster, 1957), pp. 6–7.
3. Plato, Timaeus 49a, explains the concept of the chora or spatial receptacle. I.
Newton, Opticks (New York: Dover, 1952) writes:
Does it not appear from phenomena that there is a Being incorporeal,
living, intelligent, omnipresent, who in infinite Space, as it were in his
Sensory, sees the things themselves intimately, and thoroughly perceives
them and comprehends them wholly by their immediate presence to
himself . . .? (Book III, Query 28, p. 370)
See R. H. Hurlbutt, Hume, Newton, and the Design Argument (Lincoln, NE:
University of Nebraska Press, 1985): “Infinite space is, ‘as it were’ God’s visual
field, and the things in this space are known by him in their complete inner nature
and complexity” (p. 10).
Chapter 5: Concepts of existence in philosophical logic and the
analysis of being qua being
1. The realism versus nominalism debate is discussed in a combinatorial ontology
context below in Chapter 8.
2. Useful standard expositions of modal logic are found in G. E. Hughes and M. J.
Cresswell, An Introduction to Modal Logic (London: Methuen, 1968) and Chellas,
Modal Logic: An Introduction. See also the section on “Modal Logic and Seman-
tics” in D. Jacquette (ed.), A Companion to Philosophical Logic (Oxford: Basil
Blackwell, 2002a).
3. Even strong modal systems like S
5
do not generally support the inference of logical
necessity, ~p, from the iterated logical possibility of logical necessity, ~•p. By
contrast, S
5
characteristically permits the valid inference •~p | ~p.
4. The proposition in assumption 6 in the proof on page 143, ~•›w
i
MaxCon.w
i
,
expresses the combinatorial implication whereby it must be logically possible for
there to exist a maximally consistent logically possible world, which is to say at
least one maximally consistent states-of-affairs or object–property combination
294 ONTOLOGY
among all logical possibilities. The inference is presented in terms of the weakest
modal systems; in stronger modal logics, like modal S
5
and the Brouwersche sys-
tem, the assumption is derivable, relying on combinatorial possibilities for the sim-
pler modally unqualified assumption, ›w
i
MaxCon.w
i
. (I am grateful to John Divers
for pointing out this alternative route to the conclusion in 7, without directly ap-
pealing to the iterated modality in the original assumption 6.) The essential modal
principle for these stronger logical systems appears in assumption 5c:
5. ~[•›w
i
MaxCon.w
i
÷ ›xMaxCon.w
i
] Df MaxCon
5a. ~•›w
i
MaxCon.w
i
÷ ~›xMaxCon.w
i
(5, Modal logic)
5b. •
-
›xMaxCon.w
i
÷ •~
-
›w
i
MaxCon.w
i
(6, Modal duality)
5c. •~
-
›w
i
MaxCon.w
i
÷
-
›w
i
MaxCon.w
i
(S
5
or Brouwersche)
5d. •
-
›xMaxCon.w
i
÷
-
›w
i
MaxCon.w
i
(5b,5c)
5e. ›w
i
MaxCon.w
i
÷ ~›xMaxCon.w
i
(5d, Modal duality)
6'. ›w
i
MaxCon.w
i
(Combinatorics)
7. ~›w
i
MaxCon.w
i
(5e,6)
5. It might appear, in light of the combinatorial analysis of non-actual merely logically
possible worlds as submaximally consistent, that it is obligatory to define logically
necessary truth, ~p, non-standardly as a proposition p not being false in any
logically possible world, rather than being true in every logically possible world.
The grounds for such a claim are that in a modal actualist semantics there are
countless propositions that will not describe states of affairs in any given non-actual
merely logically possible world, for which the worlds are incomplete, submaximal,
or for which they have constitutive predicational gaps. Redefining the concept of
logical necessity in this way is not required, however, as we see when we reflect
hypothetically on a dilemma concerning the applied ontology of abstract entities,
whose ontic status is yet to be determined. If there exist abstract entities, then by
definition they exist in every logically possible world, including non-actual merely
logically possible worlds; in which case, necessary truths concerning only the prop-
erties of abstract entities remain true of every logically possible world. If, on the
contrary, no abstract entities exist, then there are no logically necessary truths, but
only logically contingent truths involving the variably existent objects and states of
affairs differentially distributed across some but not all logically possible worlds.
This situation again supports the standard definition of logically necessary truth as
truth in every logically possible world, where, by hypothesis, there are no logically
necessary truths and equally no propositions that are true in every logically possible
world.
6. Inference rules for the delta A actuality operator are specified as needed for proofs
in the text further below.
7. A difference in modal scope is relevant to the argument. De re or wide modal scope
directly qualifies the modality of an object, a thing or res, as in the sentence,
“Object a is necessarily F”, whereas de dicto or narrow modal scope qualifies the
modality of a proposition, literally a saying or dictum, in which the object is
mentioned, such as, “Necessarily, object a is F”. De dicto contexts, furthermore,
including modal contexts, are generally intensional, whereas de re contexts are
extensional.
8. There is no difficulty in obtaining conclusion 20 by A inference rules. It might
appear that we could advance the following counter-derivation:
[1] Aw
@
÷ w
@
[A rule]
[2] ~[Aw
@
÷ w
@
] [[1] Necessitation]
[3] ~Aw
@
÷ ~w
@
[[2] Modal logic]
[4] ~w
@
r
-
~w
@
[[3], 20]
NOTES 295
However, the inference is invalid. The term “w
@
” does not designate a proposition,
but a world, which is to say a (maximally consistent) states-of-affairs combination.
The actual world w
@
has no truth-value, as the consequent of the conditional in
assumption [1] requires. The A inference rules explicitly apply only to propositions
as truth-value vehicles, and not to worlds, thus blocking the first step in the infer-
ence at step [1]. A counterpart version of the corresponding A rule holds for worlds
of the form: œw
i
[Aw
i
÷ ›w
k
[w
k
= w
i
]]. With this provision, we preserve the ordi-
nary linguistic equivocation between the actuality of the actual world, which is not
itself a proposition, even if it is conventionally identified with or described by a set
of propositions, and the actual truth of corresponding propositions. The alterna-
tive rule for the actual world does not support a version of the respective inference
that would otherwise contradict the conclusion in 20. The modified inference
states:
[1´] Aw
@
÷ ›w
i
[w
i
= w
@
] [A Worlds rule]
[2´] ~[Aw
@
÷ ›w
i
[w
i
= w
@
]] [[1´] Necessitation]
[3´] ~Aw
@
÷ ~›w
i
[w
i
= w
@
] [[2´] Modal logic]
[4´] ~›w
i
[w
i
= w
@
] [[3´], 20]
Conclusion [4´] is harmless, particularly when we recall that œw
i
[~w
i
÷ œp[pw
i
÷
~p]]. The proposition that ~›w
i
[w
i
=w
@
] states only that the actual world is de
dicto logically necessarily identical to some logically possible world. This is not
only not paradoxical, but intuitively true, since it does not entail that the actual
world is logically necessary de re. To say that necessarily the actual world is identi-
cal to some world is not to say that the content or condition or any constitutive
proposition of the world is logically necessary or necessarily true – as always,
leaving aside propositions about transworld universal abstract entities, if there are
any. Thus
-
[~›w
i
[w
i
= w
@
] ÷ ~w
@
]. Equally, there is no contradiction in the
conjunction of the implications of conclusion 20 with [4´]:
[5´]
-
~w
@
r ~›w
i
[w
i
= w
@
] [[4´], 20]
Part II: Applied Ontology and the Metaphysics of Science
Chapter 6: Ontological commitment (on Quine)
1. An example is an ontology of events that are explicitly said within the theory not to
be objects, or a metaphysics of properties that are objects. Quine’s requirement that
a theory first be translated into a canonical notation is doomed to distortion in the
first case if properties are to be predicated of events, but events are not represent-
able in standard symbolic logic by means of object terms or variables. It is the same
in the second case where a theory holds that properties are objects if properties
cannot legitimately be represented by predicate terms.
2. Quine, “On What There Is”, p. 1.
3. Ibid., pp. 8–9.
4. Ibid., p. 13.
5. Ibid., pp. 15–16.
6. Quine defines the concept of semantic ascent in Word and Object (Cambridge, MA:
MIT Press, 1960), pp. 271–6.
7. The criticism is developed independently by R. Cartwright, “Ontology and the
Theory of Meaning”, Philosophy of Science 21 (1954); N. Chomsky and I.
Scheffler, “What is Said to Be”, Proceedings of the Aristotelian Society 59 (1958);
296 ONTOLOGY
M. Jubien, “The Intensionality of Ontological Commitment”, Noûs 6 (1972). See
also M. P. Hodges, “Quine on ‘Ontological Commitment’”, Philosophical Studies
23 (1972).
8. G. Baker and P. M. S. Hacker, Frege: Logical Excavations (Oxford: Basil Blackwell,
1984), pp. 63–76, 88, 200–202, 280; C. Thiel, Sense and Reference in Frege’s Logic
(Dordrecht: D. Reidel, 1968) pp. 118–41; M. Dummett, The Interpretation of
Frege’s Philosophy (Cambridge, MA: Harvard University Press, 1981), pp. 323–42
and Frege: Philosophy of Language (New York: Harper and Row, 1973), especially
pp. 157–9; W. Carl, Frege’s Theory of Sense and Reference: Its Origins and Scope
(Cambridge: Cambridge University Press, 1994), pp. 96–9; M. Hahn, “The Frege
Puzzle One More Time”, in Frege: Sense and Reference One Hundred Years Later, J.
Biro and P. Kotatko (eds) (Dordrecht: Kluwer, 1995), pp. 169–83; and J. Weiner,
Frege in Perspective (Ithaca, NY: Cornell University Press, 1990), pp. 57–9, 157–61,
164–6.
9. See Chapter 1, note 5.
10. Quine, “On What There Is”, pp. 6–7.
11. Quine limits his preferred theoretical ontological domain to physical individuals
and the minimum abstract classes needed for a quasi-logicist reconstruction of
mathematics according to the programme of his “New Foundations for
Mathematical Logic”, American Mathematical Monthly 44 (1937). He explains
these commitments in Word and Object. Compare also the references indicated
below in note 18. Quine, “On Carnap’s Views on Ontology”, in The Ways of
Paradox and Other Essays (Cambridge, MA: Harvard University Press, 1976c). See
also, M. Alspector-Kelly, “On Quine on Carnap on Ontology”, Philosophical
Studies 102 (2001).
12. Against the reducibility of mathematics to classical first-order logic, see K. Gödel,
“On Formally Undecidable Propositions of Principia Mathematica and Related
Systems I”, in From Frege to Gödel: A Source Book in Mathematical Logic, 1879–
1931, Jen van Heijenoort (ed. and trans.) (Cambridge, MA: Harvard University
Press, 1967). A. Church, “An Unsolvable Problem of Elementary Number Theory”,
Bulletin of the American Mathematical Society 41 (1935). J. B. Rosser, “Extensions
of Some Theorems of Gödel and Church”, Journal of Symbolic Logic 1 (1936).
13. Quine, “On What There Is”, p. 12.
14. Ibid., p. 10.
15. Quine introduces the problem of “Gavagai” and the indeterminacy of radical
translation in Word and Object, pp. 27, 54, 72–9. A selection of the extensive
secondary literature on this important topic in Quine includes: H. Field, “Some
Thoughts on Radical Indeterminacy”, The Monist 81 (1998); J. Katz, “The Refuta-
tion of Indeterminacy”, Journal of Philosophy 85 (1988); S. Soames, “The Indeter-
minacy of Translation and the Inscrutability of Reference”, Canadian Journal of
Philosophy 29 (1999); J. Biro, “Meaning, Translation and Interpretation”,
Australasian Journal of Philosophy 59 (1981); H. J. Glock, “The Indispensability of
Translation in Quine and Davidson”, Philosophical Quarterly 43 (1993); J. F.
Harris Jr., “Indeterminacy of Translation and Analyticity”, Southern Journal of
Philosophy 14 (1976); D. Hockney, “The Bifurcation of Scientific Theories and
Indeterminacy of Translation”, Philosophy of Science 42 (1975); D. Rothbart,
“Propositions and Quine’s Indeterminacy of Radical Translation”, Dialogue 18
(1976); H. Darmstadter, “Indeterminacy of Translation and Indeterminacy of
Belief ”, Philosophical Studies 24 (1974); J. Wallace, “A Query on Radical Transla-
tion”, Southern Journal of Philosophy 68 (1971); B. M. Humphries, “Indetermi-
nacy of Translation and Theory”, Southern Journal of Philosophy 67 (1970); P. L.
Peterson, “Translation and Synonymy: Rosenberg on Quine”, Inquiry 11 (1968); J.
Hintikka, “Behavioral Criteria of Radical Translation”, Synthese 19 (1968); A.
NOTES 297
Cutrofello, “Quine and the Inscrutibility of Languages”, International Studies in
Philosophy 24 (1992); S. G. Harding, “Making Sense of Observation Sentences”,
Ratio 17 (1975); C. Boorse, “The Origins of the Indeterminacy Thesis”, Journal of
Philosophy 72 (1975); and J. Margolis, “Behaviorism and Alien Languages”,
Philosophia 3 (1973). Quine’s related topic of ontological relativity is introduced in
his landmark essay, “Ontological Relativity”, in Ontological Relativity and Other
Essays (New York: Columbia University Press, 1969). See P. Teller, “On Quine’s
Relativity of Ontology”, Canadian Journal of Philosophy 3 (1973); J. M.
Thomason, “Ontological Relativity and the Inscrutability of Reference”, Philo-
sophical Studies 22 (1971); and Quine, “On the Reasons for Indeterminacy of
Translation”, Journal of Philosophy 67 (1970).
16. Quine, Word and Object, pp. 191–232. See also Quine, “Three Grades of Modal
Involvement”, in The Ways of Paradox and Other Essays and “Reference and
Modality”, in From a Logical Point of View.
17. For a more detailed criticism of Quine’s counter-examples to quantified modal
logic, see J. Margolis, “The Planets are Nine in Number”, Canadian Journal of
Philosophy 4 (1975). Jacquette, “Intentionality and Intensionality: Quotation
Contexts and the Modal Wedge”, The Monist 59 (1986). A careful explanation of
the ambiguities of scope that are relevant to Quine’s problem is found in S. A.
Kripke, “Speaker’s Reference and Semantic Reference”, in Contemporary Perspec-
tives in the Philosophy of Language, P. A. French et al. (eds) (Minneapolis, MN:
University of Minnesota Press, 1979).
18. A. N. Whitehead and B. Russell, Principia Mathematica (3 volumes) (Cambridge:
Cambridge University Press, 1925–27). Quine, “New Foundations for Mathemati-
cal Logic”; “On the Consistency of ‘New Foundations’”, Proceedings of the
National Academy of Sciences of the USA 37 (1951); and “The Inception of NF”,
Builletin de la Socieété Mathématique de Belgique 45 (1993). J. B. Rosser, “On the
Consistency of Quine’s New Foundations for Mathematical Logic”, Journal of
Symbolic Logic 4 (1939a); “Definition by Induction in Quine’s New Foundations
for Mathematical Logic”, Journal of Symbolic Logic 4 (1939b); and “The Axiom of
Infinity in Quine’s New Foundations”, Journal of Symbolic Logic 18 (1952).
19. Quine, Word and Object, pp. 266–71; “On What There Is”, pp. 17–18; “Logic and
the Reification of Universals”, in From a Logical Point of View, pp. 102–29; “Onto-
logical Reduction and the World of Numbers”, in The Ways of Paradox and Other
Essays; and “A Logistical Approach to the Ontological Problem”, in The Ways of
Paradox and Other Essays. See J. King-Farlow, ‘Metaphysics and Choosing: Sets,
Quine, and the One’.
20. Quine, “On What There Is”, pp. 9–10.
21. Ibid., pp. 13–14.
22. Ibid., p. 17.
23. Sources in phenomenalism and sensationalism include E. B. de Condillac, An Essay
on the Origin of Human Knowledge, Being a Supplement to Mr. Locke’s Essay on
the Human Understanding, T. Nugent (trans.) (Gainesville: Scholars Facsimiles and
Reprints, 1971) and Condillac’s Treatise on the Sensations, G. Carr (trans.)
(London: The Favil Press, 1930); and E. Mach, The Analysis of Sensations, C. M.
Williams (trans.) (Chicago, IL: University of Chicago Press, 1914). See J. T.
Blackmore et al. (eds), Ernst Mach’s Vienna, 1895–1930: Or Phenomenalism as
Philosophy of Science (Dordrecht and Boston: Kluwer, 2001). The ranks of
phenomenalists also include Berkeley, Hume, Russell, Wittgenstein, Carnap, Ayer
and Broad and adherents of the sense-data movement in early twentieth-century
metaphysics.
24. Quine, “On What There Is”, pp. 16–17.
25. Critical discussions of Ockham’s razor in theory choice are found in E. Sober,
298 ONTOLOGY
Simplicity (Oxford: Clarendon Press, 1975), “The Principle of Parsimony”, British
Journal for the Philosophy of Science 32 (1981) and “Let’s Razor Ockham’s
Razor”, in Explanation and its Limits, D. Knowles (ed.) (Cambridge: Cambridge
University Press, 1990); J. J. C. Smart, “Ockham’s Razor”, in Principles of
Philosophical Reasoning, J. H. Fetzer (ed.) (Totowa: Rowman and Allenheld,
1984); M. Tweedale, “Ockham’s Supposed Elimination of Connotative Terms and
his Ontological Parsimony”, Dialogue 31 (1992); P. Abela, “Is Less Always More?
An Argument Against the Natural Ontological Attitude”, Philosophical Quarterly
46 (1996); D. Nolan, “Quantitative Parsimony”, British Journal for the Philosophy
of Science 48 (1997b); and B. Lauth, “New Blades for Ockham’s Razor”,
Erkenntnis 46 (1997).
26. Quine, “On What There Is”, p. 4.
Chapter 7: Appearance, reality, substance, transcendence
1. Parmenides, Parmenides of Elea: Fragments (Toronto: University of Toronto Press,
1984), especially the selections from Parmenides’ Proem, The Way of Truth and The
Way of Seeming. See C. C. Meinwald, Plato’s Parmenides (New York: Oxford
University Press, 1991).
2. Descartes inscribes this enigmatic Latin motto in a private notebook.
3. Descartes, Meditations on First Philosophy, Meditation 3, 4.
4. Kant’s slogan that reason without intuition (sense experience) is empty, and
intuition without concepts (innate forms of intuition or categories of pure under-
standing) is blind, succinctly summarizes his (Copernican) revolutionary synthesis
of rationalism and empiricism. Kant, Critique of Pure Reason, A51/B75.
Schopenhauer regards the distinction between phenomena (the world as it
appears), and noumena (the real world as it is in itself) as the most important
achievement of Kant’s critical idealism. In The World as Will and Representation,
E. F. J. Payne (trans.) (New York: Dover Publications, 1969), Schopenhauer writes:
“Kant’s greatest merit is the distinction of the phenomenon from the thing-in-itself,
based on the proof that between things and us there always stands the intellect, and
that on this account they cannot be known according to what they may be in them-
selves” (vol. I, pp. 417–18).
5. A. Schopenhauer, On the Fourfold Root of the Principle of Sufficient Reason, E. F.
J. Payne (trans.) (La Salle, IL: Open Court Publishing, 1974), pp. 41–2. See F. C.
White, On Schopenhauer’s Fourfold Root of the Principle of Sufficient Reason
(Leiden: E. J. Brill, 1992), for a comprehensive exposition of Schopenhauer’s
application of the principle in its limited application to phenomena or the world as
idea.
6. Berkeley avoids subjectivity in idealism only by appealing to the existence of God
as a divine infinite mind who continuously perceives all the ideas that constitute
sensible things that are only partially and discontinuously perceived by distinct
finite human minds. Subjectivity in Berkeley’s theo-empirical ontology might
nevertheless arise even on the thesis that sensible things are constituted by “con-
geries” of ideas in the mind of God, if it should turn out to be impossible in
Berkeley’s philosophy to disprove the possible existence of multiple gods with
distinct perspectives on the world of sensible things. See G. Berkeley, Three
Dialogues Between Hylas and Philonous (1710), in The Works of George Berkeley
Bishop of Cloyne (9 volumes), A. A. Luce and T. E. Jessop (eds) (London: Thomas
Nelson, 1948–57), vol. 2, especially pp. 210–14.
7. Galileo, The Assayer [Il Saggiatore, 1623], in Le Opera de Galileo Galilei, A. Favaro
(ed.) (Florence: S. A. G. Barbèra Editore, 1929–39); Descartes, Principles of
Philosophy, IV, §§188–203. R. Boyle, The Origin of Forms and Qualities (1666);
NOTES 299
J. Locke, An Essay Concerning Human Understanding [1700], P. H. Nidditch (ed.)
(Oxford: Clarendon Press, 1975), Book II, Ch. 8.
8. An excellent exposition of Schopenhauer’s fundamental distinction as it relates to
the transcendence of the thing-in-itself construed as Will is given by C. Janaway,
Self and World in Schopenhauer’s Philosophy (Oxford: Clarendon Press, 1989).
9. Berkeley, Three Dialogues Between Hylas and Philonous, pp. 154–5.
10. Supervenience and emergence are discussed in Chapter 10.
Chapter 8: Physical entities: space, time, matter and causation,
physical states of affairs and events, natural laws
1. Kant, Critique of Pure Reason A19-B73. See Kant, Prolegomena to Any Future
Metaphysics That Will be Able to Come Forward as Science, P. Carus (trans.)
(Indianapolis, IN: Hackett, 1977):
But these [idealists], and among them more particularly Berkeley,
regarded space as a mere empirical representation that, like the appear-
ances it contains, is, together with its determinations, known to us only by
means of experience or perception. I, on the contrary, prove in the first
place that space (and also time, which Berkeley did not consider) and all
its determinations can be cognized a priori by us, because, no less than
time, it inheres in us as a pure form of our sensibility before all perception
of experience and makes possible all intuition of sensibility, and therefore
all appearances. (p. 114)
2. See W. C. Salmon, (ed.), Zeno’s Paradoxes (Indianapolis, IN: the Bobs-Merrill
Company, 1970); A. Grünbaum, Modern Science and Zeno’s Paradoxes
(Middletown: Wesleyan University Press, 1967); R. Ferber, Zenons Paradoxien der
Bewegung und die Struktur von Raum und Zeit (Munich: C. H. Beck, 1981); H.
Hasse et al., Zeno and the Discovery of Incommensurables in Greek Mathematics
(New York: Arno Press, 1976); G. E. L. Owen, “Zeno and the Mathematicians”,
Proceedings of the Aristotelian Society 58 (1957–58); J. M. E. McTaggart, “The
Unreality of Time”, Mind 17 (1908) and The Nature of Existence (Grosse Point,
MI: Scholarly Press, 1968), vol. 2, ch. 33. See C. D. Broad, An Examination of
McTaggart’s Philosophy (Cambridge: Cambridge University Press, 1933–38), vol.
2, pts 1–2; G. Schlesinger, “Reconstructing McTaggart’s Argument”, Philosophy
58 (1983); W. L. Craig, “McTaggart’s Paradox and Temporal Solipsism”, Australa-
sian Journal of Philosophy 79 (2001); N. L. Oaklander, “Craig on McTaggart’s
Paradox and the Problem of Temporary Intrinsics”, Analysis 59 (1999); Q. Smith,
“The Logical Structure of the Debate About McTaggart’s Paradox”, Philosophy
Research Archives 14 (1989); and B. V. Nunn, “Differences Between A- and B-
Time”, Philosophical Inquiry 22 (2000).
3. C. S. Peirce, Letter to Welby, 12 October 1904, in Semiotics and Significs: The
Correspondence Between Charles S. Peirce and Victoria, Lady Welby, C. Hardwick
(ed.) (Bloomington, IN: Indiana University Press, 1977), on the “dynamic object”;
N. Rescher, Objectivity: The Obligations of Impersonal Reason (Notre Dame:
Notre Dame University Press, 1997), especially pp. 97–115; Husserl, Cartesian
Meditations, Third Meditation, §§27–29, pp. 60–64. See J. W. von Goethe, The
Sorrows of Young Werther, W. Rose (trans.) (London: The Scholastic Press, 1929)
Letter of 18 August, and J. J. Rousseau, The Reveries of the Solitary Walker, C.
Butterworth (trans.) (New York: Harper & Row, 1982) Fifth Walk and Seventh
Walk (on the epistemic romance of botany).
4. D. Hume, A Treatise of Human Nature [1739–40], L. A. Selby-Bigge (ed.) and P. H.
Nidditch (ed., 2nd edn) (Oxford: Clarendon Press, 1978), pp. 73–86. Hume’s
“cement of the universe” phrase appears in the appended “An Abstract of a Book
300 ONTOLOGY
Lately Published, Entituled [sic], A Treatise of Human Nature, &c.”, p. 662. J. L.
Mackie, The Cement of the Universe: A Study of Causation (Oxford: Clarendon
Press, 1982).
5. W. Heisenberg, The Physical Principles of the Quantum Theory, C. Eckart and F. C.
Hugh (trans.) (New York: Dover Publications, 1930) and Physics and Philosophy:
The Resolution in Modern Science (London: Allen and Unwin, 1959); D. Z. Albert,
Quantum Mechanics and Experience (Cambridge, MA: Harvard University Press,
1992); R. I. G. Hughes, The Structure and Interpretation of Quantum Mechanics
(Cambridge, MA: Harvard University Press, 1989); and K. R. Popper, Quantum
Theory and the Schism in Physics (Totowa: Rowman and Littlefield, 1982).
6. See D. Bohm and J. Bub, “A Proposed Solution of the Measurement Problem in
Quantum Mechanics by a Hidden Variable Theory”, Reviews of Modern Physics 38
(1966); S. Kochen and E. P. Specker, “The Problem of Hidden Variables in Quan-
tum Mechanics”, Journal of Mathematics and Mechanics 17 (1967). A survey of
controversies surrounding the interpretation of quantum anomalies is found in J. T.
Cushing and E. McMullin (eds), Philosophical Consequences of Quantum Theory:
Reflections on Bell’s Theorem (Notre Dame: University of Notre Dame Press,
1989). See also B. S. DeWitt and N. Graham, The Many-Worlds Interpretation of
Quantum Mechanics: A Fundamental Exposition (Princeton, NJ: Princeton
University Press, 1973); M. Kafatos (ed.), Bell’s Theorem, Quantum Theory, and
Conceptions of the Universe (Dordrecht: Kluwer, 1989); and B. C. Van Fraassen,
Quantum Mechanics: An Empiricist View (Oxford: Clarendon Press, 1991) and
“The Charybdis of Realism: Epistemological Implications of Bell’s Inequality”,
Synthese 52 (1982).
Chapter 9: Abstract entities, particular and universal: numbers,
sets, properties, qualities, relations, propositions, and
possibilities, logical, mathematical and metaphysical laws
1. The medieval dispute over the ontology of properties and relations is discussed by
M. H. Carré, Realists and Nominalists (London: Oxford University Press, 1946)
and M. G. Henninger, Relations: Medieval Theories 1250–1325 (Oxford:
Clarendon Press, 1989). More recent treatments of the problem are found in D. M.
Armstrong, A Theory of Universals: Universals and Scientific Realism, vol. 2 (Cam-
bridge: Cambridge University Press, 1978); M. J. Loux (ed.), Universals and Par-
ticulars: Readings in Ontology (New York: Doubleday, 1970); N. Wolterstorff, On
Universals: An Essay in Ontology (Chicago, IL: University of Chicago Press, 1970).
A recent classic treatment of the issues is offered by B. Russell, “The World of
Universals”, Chapter 8 in The Problems of Philosophy (Indianapolis, IN: Hackett,
1990), and “On the Relations of Universals and Particulars”, Chapter 9 in The
Problems of Philosophy.
2. Plato, Parmenides 132a1–133b2 and Aristotle, Metaphysics 990b1–991b9,
1038b31–1039a14. Among the items of secondary literature on this subject see T.
Scaltsas, “The Logic of the Dilemma of Participation and of the Third Man
Argument”, Apeiron 22 (1989) and “A Necessary Falsehood in the Third Man
Argument”, Phronesis 37 (1992); R. Diaz, “What is the Third Man Argument?”,
Southern Journal of Philosophy 16 (1978); M. Durrant, “Plato, the Third Man
and the Nature of the Forms”, Southern Journal of Philosophy 17 (1979); C.
Strang, “Plato and the Third Man, I”, Proceedings of the Aristotelian Society, Sup-
plement 37 (1963); D. A. Rees, “Plato and the Third Man, II”, Proceedings of the
Aristotelian Society, Supplement 37 (1963); R. J. Butler, “The Measure and Weight
of the Third Man”, Mind 72 (1963); R. Barford, “The Context of the Third Man
Argument in Plato’s Parmenides”, Journal of the History of Philosophy 16 (1978);
NOTES 301
S. Peterson, “A Reasonable Self-Predication Premise for the Third Man Argument”,
Philosophical Review 82 (1973); H. Teloh and D. J. Louzecky, “Plato’s Third Man
Argument”, Phronesis 17 (1972); S. M. Cohen, “The Logic of the Third Man”,
Philosophical Review 80 (1971); R. Shiner, “Self-Predication and the Third Man
Argument”, Journal of the History of Philosophy 8 (1970); K. W. Rankin, “Is the
Third Man Argument an Inconsistent Triad?”, Philosophical Quarterly 20 (1970)
and “The Duplicity of Plato’s Third Man”, Mind 78 (1969); G. Vlastos, “Plato’s
Third Man Argument (Parm. 132a1–b2): Text and Logic”, Philosophical Quarterly
19 (1969); “Addenda to the Third Man Argument: A Reply to Professor Sellars”,
Philosophical Review 64 (1955); and “The Third Man Arguments in the
Parmenides”, Philosophical Review 63 (1954); W. Sellars, “Vlastos and the Third
Man”, Philosophical Review 64 (1955); J. M. E. Moravcsik, “The Third Man Argu-
ment and Plato’s Theory of Forms”, Phronesis 8 (1963); N. B. Booth, “Assump-
tions Involved in the Third Man Argument”, Phronesis 3 (1958); R. S. Bluck,
“Forms as Standards”, Phronesis 2 (1957); R. E. Allen, “Participation and Predica-
tion in Plato’s Middle Dialogues”, Philosophical Review 69 (1960); R. Sharvy,
“Plato’s Causal Logic and the Third Man Argument”, Noûs 20 (1986); W. J. Prior,
“Timaeus 48e–52d and the Third Man Argument”, Canadian Journal of Philoso-
phy 9 (1983); D. P. Hunt, “How (Not) to Exempt Platonic Forms from Parmenides’
Third Man”, Phronesis 42 (1997); B. Frances, “Plato’s Response to the Third Man
Argument in the Paradoxical Exercise of the Parmenides”, Ancient Philosophy 16
(1996); P. Schweizer, “Self-Predication and the Third Man”, Erkenntnis 40
(1994); D. Davidson, “The Third Man”, Critical Inquiry 19 (1993); J. F. Malcolm,
Plato on the Self-Predication of Forms: Early and Middle Dialogues (Oxford:
Clarendon Press, 1991); F. R. Pickering, “Plato’s Third Man Arguments”, Mind 90
(1981); J. Kung, “Aristotle on Thises, Suches and the Third Man Argument”,
Phronesis 26 (1981); and R. A. Brinkley, “Plato’s Third Man and the Limits of
Cognition”, Australasian Journal of Philosophy 60 (1982).
3. G. Berkeley, A Treatise on the Principles of Human Knowledge, in The Works of
George Berkeley, vol. 2, p. 33. See also Berkeley, Three Dialogues Between Hylas
and Philonous, pp. 192–4.
4. Hume, A Treatise of Human Nature, p. 17.
5. Hume, An Enquiry Concerning Human Understanding, in Enquiries Concerning
Human Understanding and Concerning the Principles of Morals, L. A. Selby-Bigge
(ed.), 3rd edn, P. H. Nidditch (ed.) (Oxford: Clarendon Press, 1975), pp. 154–5.
6. G. Ryle, The Concept of Mind (New York: Barnes & Noble, 1949), pp. 16–17, 33,
77–9, 94, 152, 168, 206.
7. A realist position on the ontology of mathematical entities is defended by J. R.
Brown, Philosophy of Mathematics: An Introduction to the World of Proofs and
Pictures (London: Routledge, 1999). An opposing nominalistic account is repre-
sented by H. Field, Science Without Numbers: A Defense of Nominalism
(Princeton, NJ: Princeton University Press, 1980); Realism, Mathematics and
Modality (Oxford: Basil Blackwell, 1989); “Realism and Anti-Realism About
Mathematics”, Philosophical Topics 13 (1982); and “The Conceptual Contingency
of Mathematical Objects”, Mind 102 (1993). See M. Resnick, “Ontology and
Logic: Remarks on Hartry Field’s Anti-Platonist Philosophy of Mathematics”,
History and Philosophy of Logic 6 (1985); B. Hale & C. Wright, “A Reductio Ad
Surdum? Field on the Contingency of Mathematical Objects”, Mind 103 (1994);
and B. Hale, “Is Platonism Epistemologically Bankrupt?”, Philosophical Review
103 (1994). An attempt to overcome traditional epistemological difficulties by
interpreting mathematical entities as perceptible is found in P. Maddy, Realism in
Mathematics (Oxford: Clarendon Press, 1992) and Naturalism in Mathematics
(Oxford: Clarendon Press, 1997). See also D. Bonevac, Reduction in the Abstract
302 ONTOLOGY
Sciences (Indinanapolis, IN: Hackett, 1982); Quine, “Ontological Reduction and
the World of Numbers”; and S. Iwan, “An Analysis of Quine’s ‘Ontological Reduc-
tion and the World of Numbers’”, Erkenntnis 53 (2000).
8. The logic of abstraction transposes a true or false predication into a truth-value-less
property-designating predicate or property term. The standard device for this
purpose is lambda notation, whereby a predication Fa or œx[. . . x . . .] of any well-
formed internal propositional or predicational complexity is converted by lambda-
abstraction to a truth-value-less predicate term for the respective property
indicated within the context of the abstract, in these cases: /xFx or /x[. . . x . . .].
Whitehead and Russell make use of a similar reductive device in Principia
Mathematica, Part I, Section D, “The Logic of Relations”, in the theory *30 of
descriptive functions. A theory of abstraction is offered by A. Church, The Calculi
of Lambda-Conversion (Princeton, NJ: Princeton University Press, 1941).
9. Valuable sources on the ontology of properties include G. Bealer, Quality and
Concept (Oxford: Oxford University Press, 1982) and C. McGinn, Logical Proper-
ties: Identity, Existence, Predication, Necessity, Truth (Oxford: Clarendon Press,
2000). There is an extensive literature on the realism versus nominalism dispute
and the ontic status of universals in medieval through contemporary metaphysics.
Further references are indicated in notes 1 and 7.
10. Quine, Word and Object; pp. 32–51. J. Vuillement, “Quine’s Concept of Stimulus
Meaning”, Philosophic Exchange 2 (1975); F. Tersman, “Stimulus Meaning
Debunked”, Erkenntnis 49 (1998); E. Gotlind, “Stimulus Meaning”, Theoria 29
(1963); P. Ziff, “A Response to ‘Stimulus Meaning’”, Philosophical Review 79
(1970); E. S. Shirley, “Stimulus Meaning and Indeterminacy of Translation”,
Southern Journal of Philosophy 9 (1971).
11. See G. Frege, “Thoughts”, in Logical Investigations, P. T. Geach and R. H.
Stoothoff (trans.) (Oxford: Basil Blackwell, 1977); B. Bolzano, Theory of Science:
Attempt at a Detailed and in the Main Novel Exposition of Logic with Constant
Attention to Earlier Authors, R. George (ed. and trans.) (Berkeley, CA: University
of California Press, 1972), especially pp. 20–31, 171–80; C. S. Peirce, Collected
Papers of Charles Sanders Peirce (8 volumes), C. Hartshorne et al. (eds)
(Cambridge, MA: Harvard University Press, 1931–35): “The Meaning of a propo-
sition is itself a proposition. Indeed, it is no other than the very proposition which
is its meaning: it is a translation of it” (5.411-436). G. Bealer considers objections
to the traditional ontology of propositions and proposes new models for the cat-
egory in his essay, “Propositions”, Mind 107 (1998). A similar proposal for selec-
tively eliminating propositions as abstract entities in favour of thinkers expressing
cognitive attitudes toward states of affairs by using derivatively intentional sen-
tences is defended by Jubien in his essay, “Propositions and the Objects of
Thought”, Philosophical Studies 104 (2001). See also J. King, “Structured Proposi-
tions and Complex Predicates”, Noûs 29 (1995). If we agree with Jubien that
propositions do not exist, but we accept the existence of abstract sets in a realist
mathematical ontology, then the combined effect of these ontological commit-
ments has surprising implications for the metaphysics of modal logic, the ontology
of logically possible worlds, and the controversy over modal realism versus
actualism. The trouble is that, if we hold with Jubien that propositions do not exist,
then we face an obvious but previously unremarked trilemma. The propositions in
a maximally consistent proposition set {p
1
, p
2
, p
3
, . . .} are supposed collectively to
represent every state of affairs associated with a corresponding logically possible
world, w
i
. The same logically possible world w
i
can equivalently be identified or
characterized by means of the conjunction of all the propositions in the set, p
1
r p
2
r p
3
r . . .. Identifying or describing worlds alternatively as proposition sets or as
conjunctions of propositions in the set seems like a superficial logically trivial
NOTES 303
difference. A conjunction of propositions, even if infinite in extent, is itself a
proposition. If sets exist but propositions do not exist, then whether or not modal
realism is true depends on which of two apparently equivalent methods of identify-
ing, representing, or characterizing logically possible worlds we choose to adopt. If
logically possible worlds are maximally consistent proposition sets, and if sets exist
even if propositions do not exist, then, as with the default mathematical realist
commitment to the existence of even the null set, modal realism is true. If, to all
intents and purposes, we equivalently define logically possible worlds as conjunc-
tions of the propositions in the maximally consistent proposition sets identified
with or representing logically possible worlds, and if propositions do not exist, as
Jubien maintains, then modal realism is false. The nonexistence of abstract propo-
sitions in spite of the existence of abstract sets requires a new approach to possible
worlds semantics and the distinction between the actual world and non-actual
merely logically possible worlds. It requires, in the end, a satisfactory effort to ex-
plain what is meant by the concept of an actual world, and not merely the indexical
designation of this experienced world as the particular logically possible world in
which a thinker, semantic theorist or modal logician, happens to exist.
12. Classic sources include J. G. Kemeny and P. Oppenheim, “On Reduction”,
reprinted in Readings in the Philosophy of Science, B. A. Brody (ed.) (Englewood
Cliffs, NJ: Prentice Hall, 1970) and E. Nagel, “Mechanistic Explanation and
Organismic Biology”, reprinted in Readings in the Philosophy of Science (1970). A
manifesto for reductionism in the positivist unity of science programme is found in
the International Encyclopedia of Unified Science: Foundations of the Unity of
Science. See also M. Bunge, The Methodological Unity of Science (Dordrecht:
Reidel, 1973); R. Grossmann, Ontological Reduction (Bloomington, IN: Indiana
University Press, 1973); L. N. Meyer, “Science, Reduction and Natural Kinds”,
Philosophy 64 (1989); C. U. Moulines, “Ontology, Reduction, and the Unity of
Science”, in Proceedings of the Twentieth World Congress of Philosophy, 10,
Philosophy of Science, Tian Yu Cao (ed.) (Bowling Green, OH: Philosophy Docu-
mentation Center, 2001); D. J. Mossley, “The (Dis)Unity of Science: Some Ten-
sions Between the Physical, Biological and Social Sciences – A Diagnosis”, Philo-
sophical Writings 3 (1996); J. Dupré, “The Disunity of Science”, Mind 92 (1983)
and The Disorder of Things: Metaphysical Foundations of the Disunity of Science
(Cambridge, MA: Harvard University Press, 1993); J. R. Lucas, “The Unity of
Science Without Reductionism”, Acta Analytica 15 (1996); D. Davies, “Explana-
tory Disunities and the Unity of Science”, International Studies in the Philosophy of
Science 10 (1996); J. Margolis, “Nature, Culture and Persons”, Theory and
Decision 13 (1981); R. M. Burian, “Conceptual Change, Cross-Theoretical Expla-
nation, and the Unity of Science”, Synthese 32 (1975); J. Jorgensen, “Empiricism
and the Unity of Science”, Danish Yearbook of Philosophy 6 (1969); H. A.
Morgenau, “Foundations of the Unity of Science”, Philosophical Review 50
(1941); L. S. Feuer, “Mechanism, Physicalism, and the Unity of Science”, Philoso-
phy and Phenomenological Research 9 (1949); C. Morris, “The Significance of the
Unity of Science Movement”, Philosophy and Phenomenological Research 6
(1946); D. Gottlieb, “Ontological Reduction”, Journal of Philosophy 73 (1976); L.
H. Tharp, “Ontological Reduction”, Journal of Philosophy 68 (1971); R. E.
Grandy, “On What There Need Not Be”, Journal of Philosophy 66 (1969); F. W.
Kroon, “Against Ontological Reduction”, Erkenntnis 36 (1992); and M. Jubien,
“Two Kinds of Reduction”, Journal of Philosophy 66 (1969).
304 ONTOLOGY
Chapter 10: Subjectivity of mind in the world of objective
physical facts
1. J. Bickle, Psychoneural Reduction: The New Wave (Cambridge, MA: MIT Press/
Bradford Books, 1998); E. G. Boring, The Physical Dimensions of Consciousness
(New York: Appleton, 1933); D. C. Dennett, Content and Consciousness, 2nd edn
(London: Routledge & Kegan Paul, 1969) and Consciousness Explained (Boston:
Little, Brown, 1991); S. P. Stich, From Folk Psychology to Cognitive Science: The
Case Against Belief (Cambridge, MA: MIT Press/Bradford Books, 1983); H. Feigl,
The “Mental” and the “Physical”: The Essay and a Postscript (Minneapolis, MN:
University of Minnesota Press, 1967); J. Cornman, “Mental Terms, Theoretical
Terms, and Materialism”, Philosophy of Science 35 (1968); P. Feyerabend,
“Explanation, Reduction and Empiricism”, in Scientific Explanation, Space and
Time, H. Feigl and G. Maxwell (eds) (Minneapolis, MN: University of Minnesota
Press, 1962); R. Rorty, “In Defense of Eliminative Materialism”, Review of
Metaphysics 19 (1970); W. G. Lycan and G. Pappas, “What is Eliminative Materi-
alism?”, Australasian Journal of Philosophy 50 (1972); J. M. Jackson, “Why
Mental Explanations are Physical Explanations”, South African Journal of Philoso-
phy 14 (1995)’; and A. Melnyk, “Testament of a Recovering Eliminativist”,
Proceedings of the Biennial Meetings of the Philosophy of Science Association 3
(supplement) (1996).
2. See T. Nagel, “What is it Like to be a Bat?”, Philosophical Review 83 (1974); F.
Jackson, “Epiphenomenal Qualia”, Philosophical Quarterly 32 (1982); P. M.
Churchland, “Reduction, Qualia, and the Direct Inspection of Brain States”,
Journal of Philosophy 82 (1985) and “Knowing Qualia: A Reply to Jackson”, in A
Neurocomputational Perspective: The Nature of Mind and the Structure of Science,
P. M. Churchland (ed.) (Cambridge, MA: MIT Press/Bradford Books, 1990a); B.
Loar, “Phenomenal Properties”, in Mind and Cognition: A Reader, W. G. Lycan
(ed.) (Oxford: Basil Blackwell, 1990); G. Harman, “The Intrinsic Quality of
Experience”, in Philosophical Perspectives, 4: Action Theory and Philosophy of
Mind, J. E. Tomberlin (ed.) (Atascadero, CA: Ridgeview Publishing, 1990). For a
sustained discussion of the problems of qualia, including a more detailed bibliogra-
phy, see D. J. Chalmers, The Conscious Mind: In Search of a Fundamental Theory
(Oxford: Oxford University Press, 1996).
3. J. R. Searle, The Rediscovery of the Mind (Cambridge, MA: MIT Press/Bradford
Books, 1992): “On my view, if your theory results in the view that consciousness
does not exist, you have simply produced a reductio ad absurdum of the theory, and
similarly with many other views in contemporary philosophy of mind” (p. 8). A
similar incoherence undermines efforts to discount any higher-order meta-appear-
ances as something that is not really mental or psychological, but only appears to be
so. Indeed, to begin with anything plausibly described as an appearance of a mental
or psychological state to be explained away as something other than mental or psy-
chological state is logically incoherent.
4. C. V. Borst (ed.), The Mind–Brain Identity Theory (New York: St Martin’s Press,
1970); S. Christiansen and D. Turner, Folk Psychology and the Philosophy of Mind
(London: Lawrence Erlbaum, 1993); P. M. Churchland, A Neurocomputational
Perspective: The Nature of Mind and the Structure of Science (Cambridge, MA:
MIT Press/Bradford Books, 1989); U. T. Place, “Is Consciousness a Brain Proc-
ess?”, British Journal of Psychology 47 (1956); J. J. C. Smart, “Sensations and Brain
Processes”, Philosophical Review 68 (1959); P. Feyerabend, “Mental Events and the
Brain”, Journal of Philosophy 60 (1963a) and “Materialism and the Mind/Body
Problem”, Review of Metaphysics 17 (1963b); and R. Rorty, “Mind–Body Identity,
Privacy and Categories”, Review of Metaphysics 19 (1970).
NOTES 305
5. The pioneering scientific literature on behaviour includes works by Pavlov, Watson,
James, Skinner and their followers. The main philosophical developments of
logical behaviourism include Ryle, The Concept of Mind, and D. M. Armstrong, A
Materialist Theory of the Mind (London: Routledge, 1993).
6. N. Block, “Troubles With Functionalism”, in Perception & Cognition: Issues in the
Foundations of Psychology, C. W. Savage (ed.) (Minneapolis, MN: University of
Minnesota Press, 1978); T. Horgan and J. Woodward, “Folk Psychology is Here to
Stay”, Philosophical Review 94 (1985); J. Kim, “Supervenience and Nomological
Incommensurables’”, American Philosophical Quarterly 15 (1978); J. Searle,
“Minds, Brains and Programs”, The Behavioral and Brain Sciences 3 (1980); and S.
Horst, “Symbols and Computation: A Critique of the Computational Theory of
Mind”, Minds and Machines 9 (1999).
7. A concise criticism of Descartes’s substance dualism from the standpoint of the
causal interaction problem in contemporary metaphysics is offered by P. M.
Churchland, Matter and Consciousness: A Contemporary Introduction to the
Philosophy of Mind (Cambridge, MA: MIT Press/Bradford Books, 1990b), pp. 18–
21. See D. Radner, “Is There a Problem of Cartesian Interaction?”, Journal of the
History of Philosophy 23 (1985) and C. Wilson, “Sensation and Explanation: The
Problem of Consciousness in Descartes”, Nature and System 4 (1982).
8. Chalmers, The Conscious Mind; Jacquette, Philosophy of Mind (Englewood Cliffs,
NJ: Prentice Hall, 1994). Searle vehemently denies being a property dualist, but his
books Intentionality: An Essay in the Philosophy of Mind (Cambridge: Cambridge
University Press, 1983) and The Rediscovery of the Mind (Cambridge, MA: MIT
Press/Bradford Books, 1992) defend a non-reductive philosophy of mind that is
strongly reminiscent of property dualism. See Jacquette, “Searle’s Antireduction-
ism”, Facta Philosophica 4 (2002b).
9. H. Putnam, “The Meaning of ‘Meaning’”, in Mind, Language and Reality
(Cambridge: Cambridge University Press, 1975). See also, inter alia, T. Burge,
“Individualism and the Mental”, in Studies in Metaphysics, P. A. French et al. (eds)
(Minneapolis, MN: University of Minnesota Press, 1979); “Other Bodies”, in
Thought and Object, A. Woodfield (ed.) (New York: Oxford University Press,
1982a); and “Two Thought Experiments Reviewed”, Notre Dame Journal of
Formal Logic 23 (1982b); and J. A. Fodor, “Cognitive Science and the Twin-Earth
Problem”, Notre Dame Journal of Formal Logic 23 (1982).
10. An explicit analysis of supervenience applied to part–whole as well as body–mind
relations is found in J. Pollock, How to Build a Person: A Prolegomenon
(Cambridge, MA: MIT Press/Bradford Books, 1989), pp. 32–3.
11. Essential papers are collected in Kim, Supervenience and Mind: Selected Philo-
sophical Essays (Cambridge: Cambridge University Press, 1993); T. R. Grimes,
“The Myth of Supervenience”, Pacific Philosophical Quarterly 69 (1988); T.
Horgan, “From Supervenience to Superdupervenience: Meeting the Demands of a
Material World”, Mind 102 (1993); and S. Mumford, “Dispositions, Superveni-
ence and Reduction”, Philosophical Quarterly 44 (1994). Properties, entities and
events, in philosophical psychology as well as ethics and aesthetics, are sometimes
judged to be or regarded as supervenient even in the absence of any clear idea of the
relevant supervenience base on which they supervene. It is generally assumed in
such cases that the limitation is epistemic and that in principle it is possible to
determine the foundations of the relevant supervenience relations.
12. J. Margolis, Persons and Mind: The Prospects of Nonreductive Materialism
(Dordrecht: Reidel, 1978) and Philosophy of Psychology (Englewood Cliffs, NJ:
Prentice Hall, 1982); D. Davidson, “The Emergence of Thought”, Erkenntnis 51
(1999); J. L. Diaz, “Mind–Body Unity, Dual Aspect, and the Emergence of Con-
sciousness”, Philosophical Psychology 13 (2000); D. V. Newman, “Chaos, Emer-
306 ONTOLOGY
gence, and the Mind–Body Problem”, Australasian Journal of Philosophy 79
(2001); and M. Weber, “Fitness Made Physical: The Supervenience of Biological
Concepts Revisited”, Philosophy of Science 63 (1996). See the papers collected in
A. Beckermann, H. Flohr, and J. Kim (eds), Emergence or Reduction? Prospects for
Nonreductive Materialism (Berlin: Walter de Gruyter, 1992); C. Emmeche, S.
Koppe and F. Stjernfelt, “Explaining Emergence: Towards an Ontology of Levels”,
Journal for General Philosophy of Science 28 (1997); P. Humphreys, “Emergence,
Not Supervenience”, Philosophy of Science 64 (1997a) and “How Properties
Emerge”, Philosophy of Science 64 (1997b); D. H. Jones, “Emergent Properties,
Persons, and the Mind–Body Problem”, Southern Journal of Philosophy 10 (1972);
R. L. Klee, “Micro-Determinism, and Concepts of Emergence”, Philosophy of Sci-
ence 51 (1984); T. O’Connor, “Emergent Properties”, American Philosophical
Quarterly 31 (1994). M. Silberstein, “Emergence and the Mind–Body Problem”,
Journal of Consciousness Studies 5 (1998); M. Silberstein and J. McGeever, “The
Search for Ontological Emergence”, Philosophical Quarterly 49 (1999); J. J. C.
Smart, “Physicalism and Emergence”, Neuroscience 6 (1981); R. W. Sperry, “In
Defense of Mentalism and Emergent Interaction”, Journal of Mind and
Behavior 12 (1991); L. R. Vandevert, “A Measurable and Testable Brain-Based
Emergent Interactionism: An Alternative to Sperry’s Mentalist Emergent
Interactionism”, Journal of Mind and Behavior 12 (1991); J. G. Taylor, “The Emer-
gence of Mind”, Communion and Cognition 30 (1997); and P. Teller, “A Contem-
porary Look at Emergence”, in Emergence or Reduction, Beckermann et al. (eds).
Chapter 11: God, a divine supernatural mind?
1. W. I. Matson, The Existence of God (Ithaca, NY: Cornell University Press, 1965); J.
Hick, Arguments for the Existence of God (New York: Herder and Herder, 1971);
R. Swinburne, The Existence of God (Oxford: Clarendon Press, 1991); T. C.
O’Brien, Metaphysics and the Existence of God (Washington: Thomist Press,
1960); J. L. Mackie, The Miracle of Theism: Arguments for and Against the
Existence of God (Oxford: Clarendon Press, 1982); P. Vjecsner, On Proof for the
Existence of God, and Other Reflective Inquiries (New York: Penden, 1988); R. M.
Gale, On the Nature and Existence of God (Cambridge: Cambridge University
Press, 1991); D. Braine, The Reality of Time and the Existence of God: The Project
of Proving God’s Existence (Oxford: Clarendon Press, 1988).
2. Kant, Critique of Pure Reason, A599/B627–A600/B628; Anselm (of Canterbury),
Opera omnia, ad fidem codicum recensuit Franciscus Salesius Schmitt (6 volumes)
(Edinburgh: Nelson & Sons, 1945–51) and Anselm of Canterbury (4 volumes), J.
Hopkins and H. Richardson (trans.) (Toronto and New York: Edwin Mellen Press,
1974). See J. Hick and A. C. McGill (eds), The Many-Faced Argument: Recent
Studies on the Ontological Argument for the Existence of God (New York:
Macmillan, 1967); R. Brecher, Anselm’s Argument: The Logic of Divine Existence
(Aldershot: Gower, 1985) and “Hartshorne’s Modal Argument for the Existence of
God”, Ratio 17 (1976); C. Hartshorne, The Logic of Perfection and Other Essays
in Neoclassical Metaphysics (LaSalle, IL: Open Court, 1962), Anselm’s Discovery:
A Re-Examination of the Ontological Proof for God’s Existence (LaSalle, IL: Open
Court, 1965), and “Necessity”, Review of Metaphysics 21 (1967); E. Bencivenga,
Logic and Other Nonsense: The Case of Anselm and his God (Princeton, NJ:
Princeton University Press, 1993); D. P. Henry, The Logic of Saint Anselm (Oxford:
Clarendon Press, 1967); S. M. Engel, “Kant’s ‘Refutation’ of the Ontological
Argument”, Philosophy and Phenomenological Research 24 (1963); N. Malcolm,
“Anselm’s Ontological Arguments”, Philosophical Review 69 (1960); A. Plantinga,
“A Valid Ontological Argument?”, Philosophical Review 70 (1961) and “Kant’s
NOTES 307
Objection to the Ontological Argument”, Journal of Philosophy 63 (1966); G.
Schufreider, An Introduction to Anselm’s Argument (Philadelphia, PA: Temple
University Press, 1978); and J. Shaffer, “Existence, Predication and the Ontological
Argument”, Mind 71 (1962).
3. Kant, Critique of Practical Reason, pp. 127–30. See Ed. L. Miller, God and Reason:
An Invitation to Philosophical Theology, 2nd edn (Englewood Cliffs, NJ: Prentice
Hall, 1995), pp. 89–106.
4. C. G. Hunter, Darwin’s God: Evolution and the Problem of Evil (Grand Rapids:
Brazos Press, 2001); R. Swinburne, Providence and the Problem of Evil (Oxford:
Clarendon Press, 1998); B. L. Whitney, Theodicy: An Annotated Bibliography on
the Problem of Evil, 1960–1990 (New York: Garland Press, 1993); N. Pike (ed.),
God and Evil: Readings on the Theological Problem of Evil (Englewood Cliffs, NJ:
Prentice Hall, 1964); W. L. Rowe (ed.), God and the Problem of Evil (Oxford: Basil
Blackwell, 2001); M. B. Ahern, The Problem of Evil (New York: Schocken Books,
1971); M. McCord Adams and R. M. Adams (eds), The Problem of Evil (Oxford:
Oxford University Press, 1990); M. Larrimore (ed.), The Problem of Evil: A Reader
(Oxford: Basil Blackwell, 2001). In Theodicy (Indianapolis, IN: Bobbs-Merrill,
1966), Leibniz attempts to solve the problem of evil by arguing that, if God already
contains all perfections, then God can only create an imperfect world that never-
theless remains the best of all logically possible worlds, if God’s creation is to be
something other than God. This is an ingenious proposal, but one that does not
account for the high quantity, degree and extent of natural evil that prevails
throughout the actual world. Would it not have been a better world still distinct
from God if the natural evil were so slight that it would scarcely be noticed because
it did not involve physical pain or suffering?
5. The early Church Father Tertullian is reported with this attitude to have declared:
Credo, quia absurdum est (“I believe because it is absurd”).
6. See H. W. Johnstone Jr., The Problem of the Self (University Park, PA: The
Pennsylvania State University Press, 1970). Johnstone argues that considering,
overcoming and working through inconsistent beliefs is a factor in the emergence
of the self. He does not propose, however, as suggested here, extending his model
more specifically to the kinds of inconsistencies encountered in religious teachings,
let alone as an essential ingredient of religious teachings.
Chapter 12: Ontology of culture: language, art and artefacts
1. Searle, Intentionality, pp. 5, 22, 27–8, 167–8, 175–6 and “Minds, Brains, and
Programs”, pp. 422–4; also Searle’s reply to critics in the “Author’s Response”
section under the title, “Intrinsic Intentionality”, pp. 450–6 .
2. Heidegger, Being and Time, pp. 68–9.
3. The original statement of Popper’s concept of World 3 appears in K. R. Popper,
Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press,
1972), especially, pp. 31, 74–5, and 106–28. B. Carr, “Popper’s Third World”,
Philosophical Quarterly 27 (1977); W. M. Miller, “Popper’s Third World: A Meth-
odological Critique and Alternative”, Dialogue 24 (1981).
4. A sustained non-reductivist metaphysics of culture is given by Margolis, Culture
and Cultural Entities: Toward a New Unity of Science (Dordrecht and Boston:
Reidel, 1984a); Persons and Minds; Philosophy of Psychology (Englewood Cliffs,
NJ: Prentice Hall, 1984); The Language of Art and Art Criticism: Analytic Ques-
tions in Aesthetics (Detroit: Wayne State University Press, 1965); What, After All, Is
a Work of Art? Lectures in the Philosophy of Art (University Park, PA: The Pennsyl-
vania State University Press, 1999); “The Identity of a Work of Art”, Mind 68
(1959); “Works of Art as Physically Embodied and Culturally Emergent Entities”,
308 ONTOLOGY
British Journal of Aesthetics 14 (1974); “The Ontological Peculiarity of Works of
Art”, Journal of Aesthetics and Art Criticism 36 (1977); “A Strategy for a Phil-
osophy of Art” , Journal of Aesthetics and Art Criticism 37 (1979); “Artworks and
the History of Production”, Communication and Cognition 17 (1984c); “Con-
straints on the Metaphysics of Culture”, Review of Metaphysics 39 (1986);
M. Krausz and R. Shusterman (eds), Interpretation, Relativism, and the Metaphys-
ics of Culture: Themes in the Philosophy of Joseph Margolis (Amherst: Humanity
Books (Prometheus), 1999). See also Searle’s account of interpersonal intentional-
ity in The Construction of Social Reality (New York: The Free Press, 1995).
Bibliography
Abela, P. 1996. “Is Less Always More? An Argument Against the Natural Ontological
Attitude”, Philosophical Quarterly 46.
Adams, M. McCord & R. M. Adams (eds) 1990. The Problem of Evil. Oxford: Oxford
University Press.
Adams, R. M. 1991. Leibniz: Idealist, Determinist, Theist. New Haven, CT: Yale Uni-
versity Press.
Addis, L. & D. Lewis 1965. Moore and Ryle: Two Ontologists. The Hague: Martinus
Nijhoff.
Ahern, M. B. 1971. The Problem of Evil. New York: Schocken Books.
Albert, D. Z. 1992. Quantum Mechanics and Experience. Cambridge, MA: Harvard
University Press.
Allen, R. E. 1960. “Participation and Predication in Plato’s Middle Dialogues”, Philo-
sophical Review 69.
Alspector-Kelly, M. 2001. “On Quine on Carnap on Ontology”, Philosophical Studies
102.
Anselm (of Canterbury) 1945–51. Opera omnia, ad fidem codicum recensuit Franciscus
Salesius Schmitt [6 volumes]. Edinburgh: Nelson & Sons.
Anselm (of Canterbury) 1974. Anselm of Canterbury [4 volumes], J. Hopkins & H.
Richardson (trans.). Toronto and New York: Edwin Mellen Press.
Aquila, R. D. 1977. Intentionality: A Study of Mental Acts. University Park, PA: The
Pennsylvania State University Press.
Aristotle 1952. The Works of Aristotle [12 volumes], W. D. Ross (ed.). Oxford:
Clarendon Press.
Armstrong, D. M. 1978. A Theory of Universals: Universals and Scientific Realism [2
volumes]. Cambridge: Cambridge University Press.
Armstrong, D. M. 1983. What is a Law of Nature? Cambridge: Cambridge University
Press.
Armstrong, D. M. 1989a. Universals: An Opinionated Introduction. Boulder: Westview
Press.
Armstrong, D. M. 1989b. A Combinatorial Theory of Possibility. Cambridge: Cam-
bridge University Press.
Armstrong, D. M. 1993. A Materialist Theory of the Mind, rev. edn. London:
Routledge.
Armstrong, D. M. 1997. A World of States of Affairs. Cambridge: Cambridge University
Press.
Bacon, J., K. Campbell, L. Reinhardt (eds) 1993. Ontology, Causality and Mind: Essays
in Honour of D. M. Armstrong. Cambridge: Cambridge University Press.
Baert, E. 1997. Aufstieg und Untergang der Ontologie: Descartes und die
nachthomasische Philosophie. Osnabrück: Universitätsverlag Rasch.
310 ONTOLOGY
Baker, G. & P. M. S. Hacker 1984. Frege: Logical Excavations. Oxford: Basil Blackwell.
Barford, R. 1978. “The Context of the Third Man Argument in Plato’s Parmenides”,
Journal of the History of Philosophy 16.
Bealer, G. 1982. Quality and Concept. Oxford: Oxford University Press.
Bealer, G. 1998. “Propositions”, Mind 107.
Beckermann, A., H. Flohr, J. Kim (eds) 1992. Emergence or Reduction? Prospects for
Nonreductive Materialism. Berlin: Walter de Gruyter.
Bencivenga, E. 1993. Logic and Other Nonsense: The Case of Anselm and his God.
Princeton, NJ: Princeton University Press.
Benthem, J van 1985. Modal Logic and Classical Logic. Napoli: Bibliopolis.
Bergmann, G. 1979. “Sketch of an Ontological Inventory”, Journal of the British Soci-
ety for Phenomenology 10.
Bergmann, M. 1996. “A New Argument from Actualism to Serious Actualism”, Noûs 30.
Berkeley, G. 1710. A Treatise on the Principles of Human Knowledge. See Berkeley
(1948–57), volume 2.
Berkeley, G. 1713. Three Dialogues Between Hylas and Philonous. See Berkeley (1948–
57), volume 2.
Berkeley, G. 1948–57. The Works of George Berkeley Bishop of Cloyne [9 volumes], A.
A. Luce & T. E. Jessop (eds). London: Thomas Nelson & Sons.
Bickle, J. 1998. Psychoneural Reduction: The New Wave. Cambridge, MA: MIT Press/
Bradford Books.
Biro, J. 1981. “Meaning, Translation and Interpretation”, Australasian Journal of
Philosophy 59.
Blackmore, J. T., R. Itagaki, S. Tanaka (eds) 2001. Ernst Mach’s Vienna, 1895–1930: Or
Phenomenalism as Philosophy of Science. Dordrecht and Boston: Kluwer.
Blass, A. 1990. “Infinitary Combinatorics and Modal Logic”, Journal of Symbolic Logic
55.
Block, N. 1978. “Troubles With Functionalism”. In Perception & Cognition: Issues in
the Foundations of Psychology [Minnesota Studies in the Philosophy of Science, vol.
9], C. W. Savage (ed.), pp. 261–326. Minneapolis: University of Minnesota Press.
Bluck, R. S. 1957. “Forms as Standards”, Phronesis 2.
Bohm, D. & J. Bub 1966. “A Proposed Solution of the Measurement Problem in Quan-
tum Mechanics by a Hidden Variable Theory”, Reviews of Modern Physics 38.
Bolzano, B. 1972. Theory of Science: Attempt at a Detailed and in the Main Novel Ex-
position of Logic with Constant Attention to Earlier Authors. R. George (ed. and
trans.). Berkeley, CA: University of California Press.
Bonevac, D. 1982. Reduction in the Abstract Sciences. Indianapolis, IN: Hackett.
Boorse, C. 1975. “The Origins of the Indeterminacy Thesis”, Journal of Philosophy 72.
Booth, N. B. 1958. “Assumptions Involved in the Third Man Argument”, Phronesis 3.
Boring, E. G. 1933. The Physical Dimensions of Consciousness. New York: Appleton.
Borst, C. V. (ed.) 1970. The Mind-Brain Identity Theory. New York: St Martin’s Press.
Boyle, R. 1666. The Origin of Forms and Qualities. In The Works of the Honourable
Robert Boyle [6 volumes], volume 3. London: J. & F. Rivington (1772).
Bradley, F. H. 1930. Appearance and Reality: A Metaphysical Essay (9th impression,
corrected). Oxford: Clarendon Press. Originally published 1897.
Bradley, R. 1992. The Nature of All Being: A Study of Wittgenstein’s Modal Atomism.
New York: Oxford University Press.
Braine, D. 1988. The Reality of Time and the Existence of God: The Project of Proving
God’s Existence. Oxford: Clarendon Press.
Brecher, R. 1976. “Hartshorne’s Modal Argument for the Existence of God”, Ratio 17.
Brecher, R. 1985. Anselm’s Argument: The Logic of Divine Existence. Aldershot:
Gower Publishing Company.
Brentano, F. 1874. Psychologie vom empirischen Standpunkt. Leipzig: Verlag von
Duncker und Humblot.
Brentano, F. 1911. Von der Klassifikation der psychischen Phänomene. Leipzig: Verlag
von Duncker und Humblot.
BI BL I OGRAPHY 311
Brentano, F. 1924. Psychologie vom empirischen Standpunkt [2 volumes], 2nd edn,
O. Kraus (ed.). Leipzig: Felix Meiner Verlag.
Brentano, F. 1966. Die Abkehr vom Nichtrealen. Edited from the Brentano Nachlaß
with an introduction by F. Mayer-Hillebrand. Bern: Francke.
Brentano, F. 1973. Psychology from an Empirical Standpoint. O. Kraus (ed.), L. L.
McAlister (ed. English edn), A. C. Rancurello, D. B. Terrell, L. L. McAlister (trans.).
London: Routledge & Kegan Paul. Originally published 1924.
Brentano, F. 1974. Kategorienlehre. Edited with an introduction and commentary by A.
Kastil. Hamburg: Felix Meiner Verlag.
Brentano, F. 1975. On the Several Senses of Being in Aristotle, R. George (ed. and
trans.). Berkeley, CA: University of California Press.
Brentano, F. 1976. Philosophische Untersuchungen zu Raum, Zeit und Kontinuum.
Edited from the Brentano Nachlaß by Stephan Körner and Roderick M. Chisholm,
with commentary by Alfred Kastil. Hamburg: Felix Meiner Verlag.
Brentano, F. 1988. Über Ernst Machs ‘Erkenntnis und Irrtum’: mit zwei Anhängen,
Kleine Schriften über Ernst Mach, Der Brentano-Mach-Briefwechsel. Edited from the
Brentano Nachlaß with an introduction by R. M. Chisholm and J. C. Marek.
Amsterdam: Rodopi.
Bricker, P. 1996. “Isolation and Unification: The Realist Analysis of Possible Worlds”,
Philosophical Studies 84.
Bringsjord, S. 1985. “Are There Set Theoretic Possible Worlds?”, Analysis 45.
Brinkley, R. A. 1982. “Plato’s Third Man and the Limits of Cognition”, Australasian
Journal of Philosophy 60.
Broad, C. D. 1933–38. An Examination of McTaggart’s Philosophy. Cambridge:
Cambridge University Press.
Brown, J. R. 1999. Philosophy of Mathematics: An Introduction to the World of Proofs
and Pictures. London: Routledge.
Browning, D. 1973. “Quine and the Ontological Enterprise”, Review of Metaphysics 26.
Browning, D. 1990. Ontology and the Practical Arena. University Park, PA: Pennsylva-
nia State University Press.
Bubner, R., C. Cramer, R. Wiehl (eds) 1975. Semantik und Ontologie. Göttingen:
Vandenhoeck und Ruprecht.
Bunge, M. 1973. The Methodological Unity of Science. Dordrecht: D. Reidel.
Bunge, M. 1974. “The Relations of Logic and Semantics to Ontology”, Journal of
Philosophical Logic 3.
Burge, T. 1979. “Individualism and the Mental”. In Studies in Metaphysics [Midwest
Studies in Philosophy, vol. 4], P. A. French, T. E. Uehling, Jr, H. K. Wettstein (eds).
Minneapolis: University of Minnesota Press.
Burge, T. 1982a. “Other Bodies”, Thought and Object, A. Woodfield (ed.). New York:
Oxford University Press.
Burge, T. 1982b. “Two Thought Experiments Reviewed”, Notre Dame Journal of For-
mal Logic 23.
Burian, R. M. 1975. “Conceptual Change, Cross-Theoretical Explanation, and the
Unity of Science”, Synthese 32.
Butler, R. J. 1963. “The Measure and Weight of the Third Man”, Mind 72.
Campbell, K. 1990. Abstract Particulars. Oxford: Basil Blackwell.
Cantor, G. 1952. Contributions to the Founding of the Theory of Transfinite Numbers,
P. E. B. Jourdain (trans.). New York: Dover.
Carl, W. 1974. Existenz und Prädikation: Sprachanalytische Untersuchungen zu
Existenz-Aussagen. Munich: Verlag C. H. Beck.
Carl, W. 1994. Frege’s Theory of Sense and Reference: Its Origins and Scope.
Cambridge: Cambridge University Press.
Carr, B. 1977. “Popper’s Third World”, Philosophical Quarterly 27.
Carré, M. H. 1946. Realists and Nominalists. London: Oxford University Press.
Cartwright, R. 1954. “Ontology and the Theory of Meaning”, Philosophy of Science
21.
312 ONTOLOGY
Chalmers, D. J. 1996. The Conscious Mind: In Search of a Fundamental Theory.
Oxford: Oxford University Press.
Chellas, B. F. 1980. Modal Logic: An Introduction. Cambridge: Cambridge University
Press.
Chihara, C. S. 1973. Ontology and the Vicious Circle Principle. Ithaca, NY: Cornell
University Press.
Chihara, C. S. 1998. The Worlds of Possibility: Modal Realism and the Semantics of
Modal Logic. Oxford: Clarendon Press.
Chisholm, R. M. 1984. “The Primacy of the Intentional”, Synthese 61.
Chomsky, N. & I. Scheffler 1958. “What is Said to Be”, Proceedings of the Aristotelian
Society 59.
Christiansen, S. & D. Turner (eds) 1993. Folk Psychology and Philosophy of Mind. Lon-
don: Lawrence Erlbaum.
Church, A. 1935. “An Unsolvable Problem of Elementary Number Theory”, Bulletin of
the American Mathematical Society 41.
Church, A. 1941. The Calculi of Lambda–Conversion. Princeton, NJ: Princeton Univer-
sity Press.
Churchland, P. M. 1985. “Reduction, Qualia, and the Direct Inspection of Brain
States”, Journal of Philosophy 82.
Churchland, P. M. 1989. A Neurocomputational Perspective: The Nature of Mind and
the Structure of Science. Cambridge, MA: MIT Press/Bradford Books.
Churchland, P. M. 1990a. “Knowing Qualia: A Reply to Jackson”. In A
Neurocomputational Perspective: The Nature of Mind and the Structure of Science,
P. M. Churchland (ed.). Cambridge, MA: MIT Press/Bradford Books.
Churchland, P. M. 1990b. Matter and Consciousness: A Contemporary Introduction to
the Philosophy of Mind (rev. edn). Cambridge, MA: MIT Press/Bradford Books.
Code, A. 1986. “Aristotle’s Investigation of a Basic Logical Principle: Which Science
Investigates the Principle of Non-Contradiction?”, Canadian Journal of Philosophy
10 (supplement).
Coffey, P. 1938. Ontology, or the Theory of Being: An Introduction to General Meta-
physics. New York: Peter Smith.
Cohen, S. M. 1971. “The Logic of the Third Man”, Philosophical Review 80.
Condillac, É. B. de 1930. Condillac’s Treatise on the Sensations, G. Carr (trans.),
preface by H. Wildon Carr. London: The Favil Press.
Condillac, É. B. de 1971. An Essay on the Origin of Human Knowledge, Being a Supple-
ment to Mr. Locke’s Essay on the Human Understanding, T. Nugent (trans.),
introduction by R. G. Weyant. Gainesville: Scholars Facsimiles and Reprints.
Cooper, D. E. 1990. Existentialism: A Reconstruction. Oxford: Basil Blackwell.
Cornman, J. 1968. “Mental Terms, Theoretical Terms, and Materialism”, Philosophy of
Science 35.
Craig, W. L. 2001. “McTaggart’s Paradox and Temporal Solipsism”, Australasian
Journal of Philosophy 79.
Cresswell, M. J. 1988. Semantical Essays: Possible Worlds and Their Rivals. Dordrecht:
Kluwer.
Curry, H. B. with R. Feys & R. Craig 1972. Combinatory Logic. Amsterdam: North-
Holland Publishing Company.
Curry, H. B. 1977. Foundations of Mathematical Logic. New York: Dover.
Cushing, J. T. & E. McMullin (eds) 1989. Philosophical Consequences of Quantum
Theory: Reflections on Bell’s Theorem. Notre Dame: University of Notre Dame
Press.
Cutrofello, A. 1992. “Quine and the Inscrutability of Languages”, International Studies
in Philosophy 24.
Darmstadter, H. 1974. “Indeterminacy of Translation and Indeterminacy of Belief ”,
Philosophical Studies 26.
David, F. N. & D. E. Barton 1962. Combinatorial Chance. London: Charles Griffin.
Davidson, D. 1993. “The Third Man”, Critical Inquiry 19.
BI BL I OGRAPHY 313
Davidson, D. 1999. “The Emergence of Thought”, Erkenntnis 51.
Davidson, D. & J. Hintikka 1969. Words and Objections: Essays on the Work of W. V.
Quine. Dordrecht: D. Reidel.
Davies, D. 1996. “Explanatory Disunities and the Unity of Science”, International
Studies in the Philosophy of Science 10.
Dejnozka, J. 1996. The Ontology of the Analytic Tradition and its Origins: Realism and
Identity in Frege, Russell, Wittgenstein, and Quine. Lanham, MD: Littlefield Adams
Books.
Dennett, D. C. 1969.Content and Consciousness, 2nd ed. London: Routledge & Kegan
Paul.
Dennett, D. C. 1991. Consciousness Explained. Boston: Little, Brown and Company.
Descartes, R. 1628. Rules for the Direction of the Mind. See Descartes (1975), volume 1.
Descartes, R. 1637. Discourse on the Method of Rightly Conducting the Reason and
Searching for Truth in the Sciences. See Descartes (1975), volume 1.
Descartes, R. 1641. Meditations on First Philosophy. See Descartes (1975), volume 1.
Descartes, R. 1644. Principles of Philosophy. See Descartes (1975), volume 1.
Descartes, R. 1975. The Philosophical Works of Descartes [2 volumes], E. S. Haldane
and G. R. T. Ross (trans.). Cambridge: Cambridge University Press.
Deutsch, E. 1979. On Truth: An Ontological Theory. Honolulu, HI: University Press of
Hawaii.
DeWitt, B. S. & N. Graham 1973. The Many-Worlds Interpretation of Quantum Me-
chanics: A Fundamental Exposition. Princeton, NJ: Princeton University Press.
Diaz, J. L. 2000. “Mind–Body Unity, Dual Aspect, and the Emergence of Conscious-
ness”, Philosophical Psychology 13.
Diaz, R. 1978. “What is the Third Man Argument?”, Southern Journal of Philosophy
16.
Dilman, I. 1984. Quine on Ontology, Necessity and Experience: A Philosophical
Critique. London: Macmillan.
Divers, J. 1995. “Modal Fictionalism Cannot Deliver Possible Worlds Semantics”,
Analysis 55.
Dostal, R. J. 1993. “Time and Phenomenology in Husserl and Heidegger”. In The
Cambridge Companion to Heidegger, C. B. Guignon (ed.). Cambridge: Cambridge
University Press.
Dreyfus, H. L. 1991. Being-in-the-World: A Commentary on Heidegger’s Being and
Time, Division I. Cambridge, MA: MIT Press.
Dummett, M. 1973. Frege: Philosophy of Language. New York: Harper & Row.
Dummett, M. 1981. The Interpretation of Frege’s Philosophy. Cambridge, MA:
Harvard University Press.
Dummett, M. 1991. The Logical Basis of Metaphysics. Cambridge, MA: Harvard
University Press.
Dupré, J. 1983. “The Disunity of Science”, Mind 92.
Dupré, J. 1993. The Disorder of Things: Metaphysical Foundations of the Disunity of
Science. Cambridge, MA: Harvard University Press.
Durrant, M. 1979. “Plato, the Third Man and the Nature of the Forms”, Southern
Journal of Philosophy 17.
Emmeche, C., S. Koppe, F. Stjerfelt 1997. “Explaining Emergence: Towards an Ontol-
ogy of Levels”, Journal for General Philosophy of Science 28.
Engel, S. M. 1963. “Kant’s ‘Refutation’ of the Ontological Argument”, Philosophy and
Phenomenological Research 24.
Feibleman, J. K. 1968. Ontology. New York: Greenwood Press.
Feigl, H. 1967. The “Mental” and the “Physical”: The Essay and a Postscript.
Minneapolis, MN: University of Minnesota Press.
Ferber, R. 1981. Zenons Paradoxien der Bewegung und die Struktur von Raum und Zeit.
Munich: C. H. Beck.
Feuer, L. S. 1949. “Mechanism, Physicalism, and the Unity of Science”, Philosophy and
Phenomenological Research 9.
314 ONTOLOGY
Feyerabend, P. 1962. “Explanation, Reduction, and Empiricism”. In Scientific Explana-
tion, Space and Time [Minnesota Studies in the Philosophy of Science, vol. 3], H.
Feigl & G. Maxwell (eds), pp. 28–97. Minneapolis: University of Minnesota Press.
Feyerabend, P. 1963a. “Mental Events and the Brain”, Journal of Philosophy 60.
Feyerabend, P. 1963b. “Materialism and the Mind/Body Problem”, Review of Meta-
physics 17.
Field, H. 1980. Science Without Numbers: A Defense of Nominalism. Princeton, NJ:
Princeton University Press.
Field, H. 1982. “Realism and Anti-Realism About Mathematics”, Philosophical Topics
13.
Field, H. 1989. Realism, Mathematics and Modality. Oxford: Basil Blackwell.
Field, H. 1993. “The Conceptual Contingency of Mathematical Objects”, Mind 102.
Field, H. 1998. “Some Thoughts on Radical Indeterminacy”, The Monist 81.
Findlay, J. N. 1995. Meinong’s Theory of Objects and Values, edited with an introduc-
tion by D. Jacquette. Aldershot: Ashgate Publishing (Gregg Revivals) (from the 2nd
edition, Oxford University Press, 1963).
Fisk, M. 1974. Nature and Necessity: An Essay in Physical Ontology. Bloomington, IN:
Indiana University Press.
Fitch, F. B. 1974. Elements of Combinatory Logic. New Haven, CT: Yale University
Press.
Fleming, N. 1988. “Why is There Something Rather than Nothing?”, Analysis 48.
Fodor, J. A. 1982. “Cognitive Science and the Twin-Earth Problem”, Notre Dame Jour-
nal of Formal Logic 23.
Forbes, G. 1985. The Metaphysics of Modality. Oxford: Clarendon Press.
Forbes, G. 1989. Languages of Possibility: An Essay in Philosophical Logic (Aristotelian
Society Series, vol. 9). Oxford: Basil Blackwell.
Frances, B. 1996. “Plato’s Response to the Third Man Argument in the Paradoxical
Exercise of the Parmenides”, Ancient Philosophy 16.
Fräntzki, E. 1996. Daseinsontologie: erstes Hauptstück. Dettelbach: J. H. Röll.
Frege, G. 1977. “Thoughts”. In Logical Investigations, edited with a preface by P. T.
Geach; P. T. Geach & R. H. Stoothoff (trans.). Oxford: Basil Blackwell.
Gaita, R. (ed.) 1990. Value and Understanding: Essays for Peter Winch. London:
Routledge.
Gale, R. M. 1991. On the Nature and Existence of God. Cambridge: Cambridge
University Press.
Galileo 1929–39. “The Assayer” [Il Saggiatore]. In Le Opere de Galileo Galilei [20
volumes], A. Favaro (ed.). Florence: S. A. G. Barbèra Editore.
Gelven, M. 1989. A Commentary on Heidegger’s Being and Time. Dekalb, IL: Northern
Illinois University Press.
Gethmann, C. F. 1993. Dasein: Erkennen und Handeln: Heidegger im
phänomenologischen Kontext. Berlin: Walter de Gruyter.
Gilson, E. 1952. Being and Some Philosophers. Toronto: Pontifical Institute of Mediae-
val Studies.
Glock, H. J. 1993. “The Indispensability of Translation in Quine and Davidson”,
Philosophical Quarterly, 43.
Gödel, K. 1967. “On Formally Undecidable Propositions of Principia Mathematica and
Related Systems I”. In From Frege to Gödel: A Source Book in Mathematical Logic,
1879–1931, Jean van Heijenoort (ed. and trans.). Cambridge, MA: Harvard Uni-
versity Press. Originally published in 1931 as “Über formal unentscheidbare Sätze
der Principia mathematica und verwandter Systeme I”, Monatshefte für Mathematik
und Physik 38.
Goethe, J. W. von 1929. The Sorrows of Young Werther, W. Rose (trans.). London: The
Scholastics Press.
Gosselin, M. 1990. Nominalism and Contemporary Nominalism: Ontological and
Epistemological Implications of the Work of W. V. O. Quine and of N. Goodman.
Dordrecht: Kluwer.
BI BL I OGRAPHY 315
Gotlind, E. 1963. “Stimulus Meaning”, Theoria 29.
Gottlieb, D. 1976. “Ontological Reduction”, Journal of Philosophy 73.
Grandy, R. E. 1969. “On What There Need Not Be”, Journal of Philosophy 66.
Grim, P. 1986. “On Sets and Worlds: A Reply to Menzel”, Analysis 46.
Grimes, T. R. 1988. “The Myth of Supervenience”, Pacific Philosophical Quarterly 69.
Grossmann, R. 1973. Ontological Reduction. Bloomington, IN: Indiana University
Press.
Grossmann, R. 1992. The Existence of the World: An Introduction to Ontology. London
and New York: Routledge.
Grünbaum, A. 1967. Modern Science and Zeno’s Paradoxes. Middletown, CT:
Wesleyan University Press.
Guignon, C. B. (ed.) 1993. The Cambridge Companion to Heidegger. Cambridge:
Cambridge University Press.
Hahn, M. 1995. “The Frege Puzzle One More Time”. In Frege: Sense and Reference
One Hundred Years Later, J. Biro & P. Kotatko (eds). Dordrecht: Kluwer.
Hale, B. 1994. “Is Platonism Epistemologically Bankrupt?”, Philosophical Review 103.
Hale, B. 1995. “Modal Fictionalism – A Simple Dilemma”, Analysis 55.
Hale, B. & C. Wright 1994. “A Reductio ad Surdum? Field on the Contingency of Math-
ematical Objects”, Mind 103.
Hanley, C. 2000. Being and God in Aristotle and Heidegger: The Role of Method in
Thinking the Infinite. Lanham, MD: Rowman & Littlefield.
Harding, S. G. 1975. “Making Sense of Observation Sentences”, Ratio 17.
Harman, G. 1990. “The Intrinsic Quality of Experience”. In Philosophical Perspectives,
4: Action Theory and Philosophy of Mind, J. E. Tomberlin (ed.). Atascadero, CA:
Ridgeview Publishing.
Harman, G. 2002. Tool-Being: Heidegger and the Metaphysics of Objects. Chicago and
LaSalle, IL: Open Court.
Harris, J. F. Jr. 1976. “Indeterminacy of Translation and Analyticity”, Southern Journal
of Philosophy 14.
Hart, H. 1984. Understanding our World: An Integral Ontology. Lanham, MD: Univer-
sity Press of America.
Hartmann, N. 1948. Zur Grundlegung der Ontologie. Meisenheim am Glan: A. Hain.
Hartmann, N. 1953. New Ways of Ontology, R. C. Kuhn (trans.). Chicago, IL: H.
Regnery.
Hartshorne, C. 1962. The Logic of Perfection and Other Essays in Neoclassical Meta-
physics. LaSalle, IL: Open Court.
Hartshorne, C. 1965. Anselm’s Discovery: A Re-Examination of the Ontological Proof
for God’s Existence. LaSalle, IL: Open Court.
Hartshorne, C. 1967. “Necessity”, Review of Metaphysics 21.
Hasse, H., H, Scholzm, H. G. Zeuthen 1976. Zeno and the Discovery of
Incommensurables in Greek Mathematics. New York: Arno Press.
Hazen, A. 1976. “Expressive Incompleteness in Modal Logic”, Journal of Philosophical
Logic 5.
Hazen, A. 1996. “Actualism Again”, Philosophical Studies 84.
Heidegger, M. 1951. Was ist Metaphysik? (6th edn). Frankfurt am Main: A. M. V.
Klostermann.
Heidegger, M. 1953. Einführung in die Metaphysik. Tübingen: Max Niemeyer.
Heidegger, M. 1958. The Question of Being, translated with an introduction by W.
Kluback & J. T. Wilde. New York: Twayne Publishers.
Heidegger, M. 1961. An Introduction to Metaphysics, R. Manheim (trans.). Garden
City, NY: Doubleday.
Heidegger, M. 1972. Frühe Schriften. Frankfurt am Main: A. M. V. Klostermann.
Heidegger, M. 1975. Die Frage nach dem Ding: zu Kants Lehre von den transzen-
dentalen Grundsätzen. Tübingen: Max Niemeyer.
Heidegger, M. 1976a. Gesamtausgabe [85 volumes]. Frankfurt am Main: A. M. V.
Klostermann.
316 ONTOLOGY
Heidegger, M. 1976b. Existence and Being, introduction and analysis by W. Brock.
South Bend, IN: Gateway Editions.
Heidegger, M. 1979. Sein und Zeit (15th edn). Tübigen: Max Niemeyer. Originally
published 1927.
Heidegger, M. 1984. The Metaphysical Foundations of Logic, M. Heim (trans.).
Bloomington, IN: Indiana University Press.
Heidegger, M. 1996. Being and Time: A Translation of Sein und Zeit, J. Stambaugh
(trans.). Albany, NY: State University of New York Press. Originally published in
1953 by Max Niemeyer Verlag, Tübingen.
Heidegger, M. 1999. Ontology: The Hermeneutics of Facticity, J. van Buren (trans.).
Bloomington, IN: Indiana University Press.
Heine, S. 1985. Existential and Ontological Dimensions of Time in Heidegger and
Dogen. Albany, NY: State University of New York Press.
Heisenberg, W. 1930. The Physical Principles of the Quantum Theory, C. Eckart & F. C.
Hugh (trans.). New York: Dover.
Heisenberg, W. 1959. Physics and Philosophy: The Resolution in Modern Science. Lon-
don: Allen and Unwin.
Heller, M. 1990. The Ontology of Physical Objects: Four-Dimensional Hunks of
Matter. Cambridge: Cambridge University Press.
Hempel, C. G. 1973. “Science Unlimited”, Annals of the Japan Association for Philoso-
phy of Science 14.
Henninger, M. G. 1989. Relations: Medieval Theories 1250–1325. Oxford: Clarendon
Press.
Henry, D. P. 1967. The Logic of Saint Anselm. Oxford: Clarendon Press.
Hick, J. (ed.) 1964. The Existence of God. New York: Macmillan.
Hick, J. 1971. Arguments for the Existence of God. New York: Herder and Herder.
Hick, J. & A. C. McGill (eds) 1967. The Many-Faced Argument: Recent Studies on the
Ontological Argument for the Existence of God. New York: Macmillan.
Hindley, J. R., B. Lercher, J. P. Selden 1972. Introduction to Combinatory Logic
(London Mathematical Society Lecture Notes, Series 7). Cambridge: Cambridge
University Press.
Hintikka, J. 1963. “The Modes of Modality”, Acta Philosophica Fennica 16.
Hintikka, J. 1968. “Behavioral Criteria of Radical Translation”, Synthese 19.
Hintikka, J. 1975. “Impossible Possible Worlds”, Journal of Philosophical Logic 4.
Hockney, D. 1975. “The Bifurcation of Scientific Theories and Indeterminacy of
Translation”, Philosophy of Science 42.
Hodges, M. P. 1972. “Quine on ‘Ontological Commitment’”, Philosophical Studies
23.
Hookway, C. 1988. Quine: Language, Experience, and Reality. Stanford, CA: Stanford
University Press.
Horgan, T. 1993. “From Supervenience to Superdupervenience: Meeting the Demands
of a Material World”, Mind 102.
Horgan, T. & J. Woodward 1985. “Folk Psychology is Here to Stay”, Philosophical
Review 94.
Horst, S. 1999. “Symbols and Computation: A Critique of the Computational Theory
of Mind”, Minds and Machines 9.
Hoy, D. C. 1993. “Heidegger and the Hermeneutic Turn”. In The Cambridge Compan-
ion to Heidegger, C. B. Guignon (ed.). Cambridge: Cambridge University Press.
Hughes, G. E. & M. J. Cresswell 1968. An Introduction to Modal Logic. London:
Methuen.
Hughes, R. I. G. 1989. The Structure and Interpretation of Quantum Mechanics.
Cambridge, MA: Harvard University Press.
Hume, D. 1975. Enquiries Concerning Human Understanding and Concerning the
Principles of Morals, L. A. Selby-Bigge (ed.); 3rd edn, P. H. Nidditch (ed.). Oxford:
Clarendon Press. (Reprint of Essays and Treatises on Several Subjects, originally
published 1777.
BI BL I OGRAPHY 317
Hume, D. 1978. A Treatise of Human Nature, L. A. Selby-Bigge (ed.); 2nd edn, P. H.
Nidditch (ed.). Oxford: Clarendon Press. Originally published 1739–40.
Humphreys, P. 1997a. “Emergence, Not Supervenience”, Philosophy of Science 64.
Humphreys, P. 1997b. “How Properties Emerge”, Philosophy of Science 64.
Humphries, B. M. 1970. “Indeterminacy of Translation and Theory”, Southern Journal
of Philosophy 67.
Hunt, D. P. 1997. “How (Not) to Exempt Platonic Forms from Parmenides’ Third
Man”, Phronesis 42.
Hunter, C. G. 2001. Darwin’s God: Evolution and the Problem of Evil. Grand Rapids,
MI: Brazos Press.
Hurlbutt, R. H. 1985. Hume, Newton, and the Design Argument (rev. edn). Lincoln,
NE: University of Nebraska Press.
Husserl, E. 1962. Ideas: General Introduction to Pure Phenomenology, W. R. Boyce
Gibson (trans.). New York: Collier Books.
Husserl, E. 1966. Logische Untersuchungen (2nd edn), G. Patzig (ed.). Göttingen:
Vandenhoeck & Ruprecht.
Husserl, E. 1977. Cartesian Meditations: An Introduction to Phenomenology, D. Cairns
(trans.). The Hague: Martinus Nijhoff.
Iwan, S. 2000. “An Analysis of Quine’s ‘Ontological Reduction and the World of
Numbers’”, Erkenntnis 53.
Jackson, F. 1982. “Epiphenomenal Qualia”, Philosophical Quarterly 32.
Jackson, J. M. 1995. “Why Mental Explanations are Physical Explanations”, South
African Journal of Philosophy 14.
Jacoby, G. 1993. Allgemeine Ontologie der Wirklichkeit. Tübingen: Max Niemeyer.
Jacquette, D. 1986. “Intentionality and Intensionality: Quotation Contexts and the
Modal Wedge”, The Monist 59.
Jacquette, D. 1994. Philosophy of Mind. Englewood Cliffs, NJ: Prentice Hall.
Jacquette, D. (ed.) 1996. Schopenhauer, Philosophy, and the Arts. Cambridge:
Cambridge University Press.
Jacquette, D. (ed.) 2002a. A Companion to Philosophical Logic. Oxford: Basil
Blackwell.
Jacquette, D. 2002b. “Searle’s Antireductionism”, Facta Philosophica 4.
Jager, T. 1982. “An Actualist Semantics for Quantified Modal Logic”, Notre Dame Jour-
nal of Formal Logic 23.
Janaway, C. 1989. Self and World in Schopenhauer’s Philosophy. Oxford: Clarendon
Press.
Johansson, I. 1989. Ontological Investigations. London: Routledge.
Johnstone, H. W. Jr. 1970. The Problem of the Self. University Park, PA: The Pennsylva-
nia State University Press.
Jones, D. H. 1972. “Emergent Properties, Persons, and the Mind–Body Problem”,
Southern Journal of Philosophy 10.
Jorgensen, J. 1969. “Empiricism and Unity of Science”, Danish Yearbook of Philosophy
6.
Jubien, M. 1969. “Two Kinds of Reduction”, Journal of Philosophy 66.
Jubien, M. 1972. “The Intensionality of Ontological Commitment”, Noûs 6.
Jubien, M. 1988. “Problems With Possible Worlds”. In Philosophical Analysis, D. F.
Austin (ed.). Dordrecht: Kluwer.
Jubien, M. 1993. Ontology, Modality, and the Fallacy of Reference. Cambridge:
Cambridge University Press.
Jubien, M. 1996. “Actualism and Iterated Modalities”, Philosophical Studies 84.
Jubien, M. 2001. “Propositions and the Objects of Thought”, Philosophical Studies
104.
Kafatos, M. (ed.) 1989. Bell’s Theorem, Quantum Theory, and Conceptions of the
Universe. Dordrecht: Kluwer.
Kaminsky, J. 1969. Language and Ontology. Carbondale, IL: Southern Illinois Univer-
sity Press.
318 ONTOLOGY
Kant, I. 1949. Critique of Practical Reason and Other Writings in Moral Philosophy,
L. White Beck (ed. and trans.). Chicago, IL: University of Chicago Press.
Kant, I. 1965. Critique of Pure Reason, N. Kemp Smith (trans.). New York: St Martin’s
Press.
Kant, I. 1977. Prolegomena to Any Future Metaphysics That Will be Able to Come For-
ward as Science, P. Carus (trans.), J. W. Ellington (rev.). Indianapolis, IN: Hackett.
Kanthack, K. 1962. Nicolai Hartmann und das Ende der Ontologie. Berlin: Walter de
Gruyter.
Katz, J. 1988. “The Refutation of Indeterminacy”, Journal of Philosophy 85.
Kemeny, J. G. & P. Oppenheim 1970. “On Reduction”. Reprinted in Readings in the
Philosophy of Science, B. A. Brody (ed.). Englewood Cliffs, NJ: Prentice Hall.
Kim, J. 1978. “Supervenience and Nomological Incommensurables”, American
Philosophical Quarterly 15.
Kim, J. 1984. “Concepts of Supervenience”, Philosophy and Phenomenological
Research 45.
Kim, J. 1986. “Possible Worlds and Armstrong’s Combinatorialism”, Canadian Journal
of Philosophy 16.
Kim, J. 1987. “‘Strong’ and ‘Global’ Supervenience Revisited”, Philosophy and
Phenomenological Research 48.
Kim, J. 1990. “Supervenience as a Philosophical Concept”, Metaphilosophy 21.
Kim, J. 1993. Supervenience and Mind: Selected Philosophical Essays. Cambridge:
Cambridge University Press.
King, J. 1995. “Structured Propositions and Complex Predicates”, Noûs 29.
King-Farlow, J. 1999. “Metaphysics and Choosing: Sets, Quine, and the One”, Iyyun:
The Jerusalem Philosophical Quarterly 48.
Kisiel, T. 1973. “On the Dimensions of a Phenomenology of Science in Husserl and the
Young Dr. Heidegger”, Journal of the British Society for Phenomenology 4.
Klee, R. L. 1984. “Micro-Determinism and Concepts of Emergence”, Philosophy of
Science 51.
Kochen, S. & E. P. Specker 1967. “The Problem of Hidden Variables in Quantum
Mechanics”, Journal of Mathematics and Mechanics 17.
Kockelmans, J. J. (ed.) 1986. A Companion to Martin Heidegger’s “Being and Time”.
Washington, DC: Center for Advanced Research in Phenomenology and University
Press of America.
Kockelmans, J. J. 1989. Heidegger’s “Being and Time”: The Analytic of Dasein as
Fundamental Ontology. Lanham, MD: Center for Advanced Research in Phenom-
enology and University Press of America.
Krausz, M. & R. Shusterman (eds) 1999. Interpretation, Relativism, and the Metaphys-
ics of Culture: Themes in the Philosophy of Joseph Margolis. Amherst: Humanity
Books (Prometheus).
Kripke, S. A. 1963a. “Semantical Considerations on Modal Logics”, Acta Philosophica
Fennica 16.
Kripke, S. A. 1963b. “Semantical Analysis of Modal Logic I: Normal Modal
Propositional Calculi”, Zeitschrift für mathematische Logik und Grundlagen der
Mathematik 9.
Kripke, S. A. 1979. “Speaker’s Reference and Semantic Reference”. In Contemporary
Perspectives in the Philosophy of Language, P. A. French, T. E. Uehling Jr., H. K.
Wettstein (eds). Minneapolis, MN: University of Minnesota Press.
Kripke, S. A. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press.
Kroon, F. W. 1992. “Against Ontological Reduction”, Erkenntnis 36.
Kuhn, T. 1962. The Structure of Scientific Revolutions. Chicago, IL: University of Chi-
cago Press.
Kung, J. 1981. “Aristotle on Thises, Suches and the Third Man Argument”, Phronesis 26.
Küng, G. 1963. Ontologie und logistische Analyse der Sprache: Eine Untersuchung zur
zeitgenössischen Universaliendiskussion. Vienna: Springer-Verlag.
Langan, T. 1996. Being and Truth. Columbia, MO: University of Missouri Press.
BI BL I OGRAPHY 319
Lango, J. W. 1972. Whitehead’s Ontology. Albany, NY: State University of New York
Press.
Larrimore, M. (ed.) 2001. The Problem of Evil: A Reader. Oxford: Basil Blackwell.
Lauth, B. 1997. “New Blades for Occam’s Razor”, Erkenntnis 46.
Leblanc, H. 1973. ‘”On Dispensing with Things and Worlds”. In Logic and Ontology:
Studies in Contemporary Philosophy, M. K. Munitz (ed.). New York: New York
University Press.
Leblanc, H. 1982. Existence, Truth, and Provability. Albany, NY: State University of
New York Press.
Leibniz, G. W. 1902. Discourse on Metaphysics; Correspondence With Arnauld,
Monadology, G. R. Montgomery (trans.). LaSalle, IL: Open Court.
Leibniz, G. W. 1966. Theodicy, E. M. Huggard (trans.). Indianapolis, IN: Bobbs-
Merrill.
Leibniz, G. W. 1973a. “Necessary and Contingent Truth”. See Leibniz 1973f.
Leibniz, G. W. 1973b. “On Freedom” . See Leibniz 1973f.
Leibniz, G. W. 1973c. “A Letter on Freedom” . See Leibniz 1973f.
Leibniz, G. W. 1973d. “On the Principle of Indiscernibles” . See Leibniz 1973f.
Leibniz, G. W. 1973e. “On the Ultimate Origination of Things” . See Leibniz 1973f.
Leibniz, G. W. 1973f. Leibniz: Philosophical Writings, G. H. R. Parkinson (ed.), M.
Morris & G. H. R. Parkinson (trans.). London: J. M. Dent & Son.
Leibniz, G. W. 1989. De Arte Combinatoria. In Sämtliche Schriften und Briefe, series VI
[16 volumes], volume 1. Berlin: Akademie-Verlag. Originally published in 1666 as
Dissertatio.
Lewis, C. I. 1912. “Implication and the Algebra of Logic”, Mind 21.
Lewis, C. I. 1913. “Interesting Theorems in Symbolic Logic”, Journal of Philosophy 10.
Lewis, C. I. 1914. “The Matrix Algebra for Implication”, Journal of Philosophy 11.
Lewis, C. I. 1918. A Survey of Symbolic Logic. Berkeley, CA: University of California
Press.
Lewis, C. I. 1920. “Strict Implication: An Emendation”, Journal of Philosophy 17.
Lewis, C. I. & C. H. Langford 1959. Symbolic Logic, 2nd edn. New York: Dover.
Orginally published 1932.
Lewis, D. K. 1968. “Counterpart Theory and Quantified Modal Logic”, Journal of
Philosophy 65.
Lewis, D. K. 1973. Counterfactuals. Oxford: Basil Blackwell.
Lewis, D. K. 1986. On the Plurality of Worlds. Oxford: Basil Blackwell.
Loar, B. 1990. “Phenomenal Properties”. In Mind and Cognition: A Reader, W. G. Lycan
(ed.). Oxford: Basil Blackwell.
Locke, J. 1975. An Essay Concerning Human Understanding, P. H. Nidditch (ed.).
Oxford: Clarendon Press. Originally published 1700.
Loux, M. J. (ed.) 1970. Universals and Particulars: Readings in Ontology. New York:
Doubleday.
Loux, M. J. 1978. Substance and Attribute: A Study in Ontology. Dordrecht: D. Reidel.
Loux, M. J. (ed.) 1979. The Possible and the Actual. Ithaca, NY: Cornell University Press.
Lovejoy, A. O. 1964. The Great Chain of Being: A Study of the History of an Idea (The
William James Lectures Delivered at Harvard University, 1933). Cambridge:
Harvard University Press.
Lucas, J. R. 1996. “The Unity of Science Without Reductionism”, Acta Analytica 15.
Luijpen, W. 1969. Existential Phenomenology. Pittsburgh, PA: Duquesne University
Press.
Lycan, W. G. (ed.) 1990. Mind and Cognition: A Reader. Oxford: Basil Blackwell.
Lycan, W. G. & G. Pappas 1972. “What is Eliminative Materialism?”, Australasian
Journal of Philosophy 50.
Mach, E. 1914. The Analysis of Sensations, C. M. Williams (trans.). Chicago, IL:
University of Chicago Press.
Mackie, J. L. 1974. The Cement of the Universe: A Study of Causation. Oxford:
Clarendon Press.
320 ONTOLOGY
Mackie, J. L. 1982. The Miracle of Theism: Arguments For and Against the Existence of
God. Oxford: Clarendon Press.
MacMahon, P. A. 1984. Combinatory Analysis. New York: Chelsea.
Maddy, P. 1992. Realism in Mathematics. Oxford: Clarendon Press.
Maddy, P. 1997. Naturalism in Mathematics. Oxford: Clarendon Press.
Malcolm, J. F. 1991. Plato on the Self-Predication of Forms: Early and Middle
Dialogues. Oxford: Clarendon Press.
Malcolm, N. 1960. “Anselm’s Ontological Arguments”, Philosophical Review 69.
Marcus, R. B. 1993. Modalities: Philosophical Essays. New York: Oxford University
Press.
Mares, E. D. 1997. “Who’s Afraid of Impossible Worlds?”, Notre Dame Journal of
Formal Logic 38.
Margolis, J. 1959. “The Identity of a Work of Art”, Mind 68.
Margolis, J. 1965. The Language of Art and Art Criticism: Analytic Questions in
Aesthetics. Detroit: Wayne State University Press.
Margolis, J. 1973. “Behaviorism and Alien Languages”, Philosophia 3.
Margolis, J. 1974. “Works of Art as Physically Embodied and Culturally Emergent
Entities”, British Journal of Aesthetics 14.
Margolis, J. 1975. “The Planets are Nine in Number”, Canadian Journal of Philosophy
4.
Margolis, J. 1977. “The Ontological Peculiarity of Works of Art”, Journal of Aesthetics
and Art Criticism 36.
Margolis, J. 1978. Persons and Minds: The Prospects of Nonreductive Materialism
(Boston Studies in the Philosophy of Science, 57). Dordrecht: D. Reidel.
Margolis, J. 1979. “A Strategy for a Philosophy of Art”, Journal of Aesthetics and Art
Criticism 37.
Margolis, J. 1980. Art and Philosophy. Atlantic Highlands, NJ: Humanities Press.
Margolis, J. 1981. “Nature, Culture and Persons”, Theory and Decision 13.
Margolis, J. 1984a. Culture and Cultural Entities: Toward a New Unity of Science.
Dordrecht and Boston: D. Reidel.
Margolis, J. 1984b. Philosophy of Psychology. Englewood Cliffs, NJ: Prentice Hall.
Margolis, J. 1984c. “Artworks and the History of Production”, Communication and
Cognition 17.
Margolis, J. 1986. “Constraints on the Metaphysics of Culture”, Review of Metaphysics
39.
Margolis, J. 1999. What, After All, Is a Work of Art? Lectures in the Philosophy of Art.
University Park, PA: The Pennsylvania State University Press.
Marx, W. 1954. The Meaning of Aristotle’s “Ontology”. The Hague: Martinus Nijhoff.
Matson, W. I. 1965. The Existence of God. Ithaca, NY: Cornell University Press.
Mayer, R. 1981. Ontologische Aspekte der Nominalsemantik. Tübingen: Max
Niemeyer.
McGinn, C. 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth.
Oxford: Clarendon Press.
McKeon, M. 1996. “Logical Truth in Modal Logic”, Pacific Philosophical Quarterly
77.
McLaughlin, B. & M. Tye 1998. “Externalism, Twin-Earth, and Self-Knowledge”. In
Knowing Our Own Minds, C. Wright, B. C. Smith & C. MacDonald (eds). Oxford:
Oxford University Press.
McMichael, A. 1983a. “A New Actualist Modal Semantics”, Journal of Philosophical
Logic 12.
McMichael, A. 1983b. “A Problem for Actualism About Possible Worlds”, Philosophical
Review 92.
McTaggart, J. M. E. 1908. “The Unreality of Time”, Mind 17.
McTaggart, J. M. E. 1968. The Nature of Existence [2 volumes]. Grosse Pointe, MI:
Scholarly Press. (Originally published 1921–27, Cambridge University Press).
Meixner, U. 1997. Axiomatic Formal Ontology. Kluwer.
BI BL I OGRAPHY 321
Melcic, D. 1986. Heideggers Kritik der Metaphysik und das Problem der Ontologie.
Würzburg: Königshausen & Neumann.
Meinong, A. 1969–78. Alexius Meinong Gesamtausgabe [8 volumes], R. Haller & R.
Kindinger (eds), in collaboration with R. M. Chisholm. Graz: Akademische Druck-
u. Verlagsanstalt.
Meinwald, C. C. 1991. Plato’s Parmenides. New York: Oxford University Press.
Melnyck, A. 1996. “Testament of a Recovering Eliminativist”, Proceedings of the
Biennial Meetings of the Philosophy of Science Association 3 (supplement).
Mendelson, E. 1964. Introduction to Mathematical Logic. New York: D. Van Nostrand.
Mensch, J. R. 1981. The Question of Being in Husserl’s Logical Investigations. The
Hague and Boston: Kluwer.
Menzel, C. 1986. “On Set Theoretic Possible Worlds”, Analysis 46.
Menzel, C. 1990. “Actualism, Ontological Commitment, and Possible Worlds Seman-
tics”, Synthese 85.
Merleau-Ponty, M. 1962. The Phenomenology of Perception, C. Smith (trans.). New
York: The Humanities Press.
Meyer, L. N. 1989. “Science, Reduction and Natural Kinds”, Philosophy 64.
Miller, Ed. L. 1995. God and Reason: An Invitation to Philosophical Theology, 2nd edn.
Englewood Cliffs, NJ: Prentice Hall.
Miller, W. M. 1981. “Popper’s Third World: A Methodological Critique and Alterna-
tive”, Dialogue 24.
Mohanty, J. N. 1972. The Concept of Intentionality. St. Louis, MO: Warren H. Green.
Moran, D. 2000. “Heidegger’s Critique of Husserl’s and Brentano’s Accounts of Inten-
tionality”, Inquiry 43.
Moravcsik, J. M. E. 1963. “The Third Man Argument and Plato’s Theory of Forms”,
Phronesis 8.
Moreland, J. P. 1985. Universals, Qualities, and Quality-Instances: A Defense of
Realism. Lanham, MD: University Press of America.
Morewedge, P. 1982. Philosophies of Existence, Ancient and Medieval. New York:
Fordham University Press.
Morgenau, H. A. 1941. “Foundations of the Unity of Science”, Philosophical Review
50.
Morris, C. 1946. “The Significance of the Unity of Science Movement”, Philosophy and
Phenomenological Research 6.
Mortensen, C. 1986. “Explaining Existence”, Canadian Journal of Philosophy 16.
Mossley, D. J. 1996. “The (Dis)Unity of Science: Some Tensions Between the Physical,
Biological and Social Sciences – A Diagnosis”, Philosophical Writings 3.
Moulines, C. U. 2001. “Ontology, Reduction, and the Unity of Science”. In The Pro-
ceedings of the Twentieth World Congress of Philosophy, 10, Philosophy of Science,
Tian Yu Cao (ed.). Bowling Green, OH: Philosophy Documentation Center.
Mulligan, K. (ed.) 1992. Language, Truth and Ontology. Dordrecht: Kluwer.
Mumford, S. 1994. “Supervenience and Reduction”, Philosophical Quarterly 44.
Nagel, E. 1970. “Mechanistic Explanation and Organismic Biology”. Reprinted in
Readings in the Philosophy of Science, B. A. Brody (ed.). Englewood Cliffs, NJ:
Prentice Hall.
Nagel, T. 1974. “What is it Like to be a Bat?”, Philosophical Review 83.
Neurath, O., G. De Santillana, E. Zillsel 1941. International Encyclopedia of Unified
Science: Foundations of the Unity of Science. Chicago, IL: University of Chicago
Press.
Newman, D. V. 2001. “Chaos, Emergence, and the Mind–Body Problem”, Australasian
Journal of Philosophy 79.
Newton, I. 1952. Opticks, 4th edn. New York: Dover.
Nolan, D. 1997a. “Impossible Worlds: A Modest Approach”, Notre Dame Journal of
Formal Logic 38.
Nolan, D. 1997b. “Quantitative Parsimony”, British Journal for the Philosophy of
Science 48.
322 ONTOLOGY
Nozick, R. 1981. Philosophical Explanations. Oxford: Clarendon Press.
Nunn, B. V. 2000. “Differences Between A- and B-Time”, Philosophical Inquiry 22.
Oaklander, N. L. 1999. “Craig on McTaggart’s Paradox and the Problem of Temporary
Intrinsics”, Analysis 59.
O’Brien, T. C. 1960. Metaphysics and the Existence of God. Washington: Thomist
Press.
O’Connor, T. 1994. “Emergent Properties”, American Philosophical Quarterly 31.
Owen, G. E. L. 1957–58. “Zeno and the Mathematicians”, Proceedings of the Aristote-
lian Society 58.
Owens, J. 1978. The Doctrine of Being in the Aristotelian Metaphysics: A Study in the
Greek Background of Mediaeval Thought, preface by Etienne Gilson, 3rd edn, rev.
Toronto: Pontifical Institute of Mediaeval Studies.
Parfit, D. 1992. “The Puzzle of Reality: Why Does the Universe Exist?”, Times Literary
Supplement, 3 July. Expanded version, “Why Anything? Why This?”, London
Review of Books 22 January and 5 February (1998)).
Parkinson, G. H. R. 1965. Logic and Reality in Leibniz’s Metaphysics. Oxford:
Clarendon Press.
Parmenides 1984. Parmenides of Elea: Fragments. Text and translation with an
introduction by D. Gallop. Toronto: University of Toronto Press.
Peirce, C. S. 1931–35. Collected Papers of Charles Sanders Peirce [8 volumes], C.
Hartshorne, P. Weiss, A. W. Burks (eds). Cambridge, MA: Harvard University Press.
Peirce, C. S. 1977. Semiotics and Significs: The Correspondence Between Charles S.
Peirce and Victoria, Lady Welby, C. Hardwick (ed.). Bloomington, IN: Indiana
University Press.
Pelletier, F. J. 1983. “Plato on Not-Being: Some Interpretations of the ‘Symploki Eidon’
(259e) and Their Relation to Parmenides’ Problem”, Midwest Studies in Philosophy
8.
Pelletier, F. J. 1990. Parmenides, Plato, and the Semantics of Not-Being. Chicago, IL:
University of Chicago Press.
Peterson, P. L. 1968. “Translation and Synonymy: Rosenberg on Quine”, Inquiry 11.
Peterson, S. 1973. “A Reasonable Self-Predication Premise for the Third Man
Argument”, Philosophical Review 82.
Philipse, H. 1998. Heidegger’s Philosophy of Being: A Critical Interpretation. Princeton,
NJ: Princeton University Press.
Pickering, F. R. 1981. “Plato’s Third Man Arguments”, Mind 90.
Pike, N. (ed.) 1964.. God and Evil: Readings on the Theological Problem of Evil.
Englewood Cliffs, NJ: Prentice Hall.
Place, U. T. 1956. “Is Consciousness a Brain Process?”, British Journal of Psychology 47.
Plantinga, A. 1961. “A Valid Ontological Argument?”, Philosophical Review 70.
Plantinga, A. 1966. “Kant’s Objection to the Ontological Argument”, Journal of
Philosophy 63.
Plantinga, A. 1974. The Nature of Necessity. Oxford: Oxford University Press.
Plantinga, A. 1979. “Actualism and Possible Worlds”. In The Possible and the Actual, M.
J. Loux (ed.). Ithaca, NY: Cornell University Press.
Plato 1997. Complete Works, J. M. Cooper (ed.). Indianapolis, IN: Hackett.
Poli, R. & P. Simons (eds) 1996. Formal Ontology. Dordrecht: Kluwer.
Pollock, J. 1989. How to Build a Person: A Prolegomenon. Cambridge, MA: MIT Press/
Bradford Books.
Popper, K. R. 1972. Objective Knowledge: An Evolutionary Approach. Oxford:
Clarendon Press.
Popper, K. R. 1982. Quantum Theory and the Schism in Physics. Totowa: Rowman and
Littlefield.
Priest, G. (ed.) 1997. “Impossible Worlds”, Notre Dame Journal of Formal Logic 38
(guest-edited issue).
Prior, W. J. 1983. “Timaeus 48e-52d and the Third Man Argument”, Canadian Journal
of Philosophy 9.
BI BL I OGRAPHY 323
Putnam, H. 1975. “The Meaning of ‘Meaning’”. In Mind, Language, and Reality. Cam-
bridge: Cambridge University Press.
Quine, W. V. O. 1937. “New Foundations for Mathematical Logic”, American Math-
ematical Monthly 44.
Quine, W. V. O. 1951. “On the Consitency of ‘New Foundations’”, Proceedings of the
National Academy of Sciences of the USA 37.
Quine, W. V. O. 1960. Word and Object. Cambridge, MA: MIT Press.
Quine, W. V. O. 1963a. “On What There Is”. In From a Logical Point of View, 2nd edn,
rev. New York: Harper & Row.
Quine, W. V. O. 1963b. “Logic and the Reification of Universals”. In From a Logical
Point of View, 2nd edn, rev. New York: Harper & Row.
Quine, W. V. O. 1963c. “Reference and Modality”. In From a Logical Point of View, 2nd
edn, rev. New York: Harper & Row.
Quine, W. V. O. 1969. “Ontological Relativity”. In Ontological Relativity and Other
Essays. New York: Columbia University Press.
Quine, W. V. O. 1970. “On the Reasons for Indeterminacy of Translation”, Journal of
Philosophy 67.
Quine, W. V. O. 1976a. “Three Grades of Modal Involvement”. In The Ways of Paradox
and Other Essays, revised and enlarged edition. Cambridge, MA: Harvard Univer-
sity Press.
Quine, W. V. O. 1976b. “A Logistical Approach to the Ontological Problem”. In The
Ways of Paradox and Other Essays, revised and enlarged edition. Cambridge, MA:
Harvard University Press.
Quine, W. V. O. 1976c. “On Carnap’s Views on Ontology”. In The Ways of Paradox and
Other Essays, revised and enlarged edition. Cambridge, MA: Harvard University
Press.
Quine, W. V. O. 1976d. “Ontological Reduction and the World of Numbers”. In The
Ways of Paradox and Other Essays, revised and enlarged edition. Cambridge, MA:
Harvard University Press.
Quine, W. V. O. 1976e. “On Multiplying Entities”. In The Ways of Paradox and Other
Essays, revised and enlarged edition. Cambridge, MA: Harvard University Press.
Quine, W. V. O. 1976f. “Ontological Remarks on the Propositional Calculus”. In The
Ways of Paradox and Other Essays, revised and enlarged edition. Cambridge, MA:
Harvard University Press.
Quine, W. V. O. 1993. “The Inception of NF”, Bulletin de la Société Mathématique de
Belgique, serie B, 45.
Radner, D. 1985. “Is There a Problem of Cartesian Interaction?”, Journal of the History
of Philosophy 23.
Rankin, K. W. 1969. “The Duplicity of Plato’s Third Man”, Mind 78.
Rankin, K. W. 1970. “Is the Third Man Argument an Inconsistent Triad?”, Philosophi-
cal Quarterly, 20.
Ray, G. 1996. “Ontology-Free Modal Semantics”, Journal of Philosophical Logic 25.
Rees, D. A. 1963. “Plato and the Third Man, II”, Proceedings of the Aristotelian Society,
Supplement 37.
Rescher, N. 1997. Objectivity: The Obligations of Impersonal Reason. Notre Dame:
Notre Dame University Press.
Rescher, N. & R. Brandom 1979. The Logic of Inconsistency: A Study in Non-Standard
Possible-World Semantics and Ontology. Totowa: Rowman and Littlefield.
Resnick, M. 1985. “Ontology and Logic: Remarks on Hartry Field’s Anti-Platonist
Philosophy of Mathematics”, History and Philosophy of Logic 6.
Richardson, W. J. (ed.) 1963. Heidegger: Through Phenomenology to Thought. The
Hague: Martinus Nijhoff.
Riefstahl, H. 1983. Ontische Strukturen. Mannheim: Verlag der Humboldt-Gesellschaft
für Wissenschaft, Kunst und Bildung.
Riordan, J. 1958. An Introduction to Combinatorial Analysis. New York: Wiley.
Rorty, R. 1965. “Mind–Body Identity, Privacy and Categories”, Review of Metaphysics 19.
324 ONTOLOGY
Rorty, R. 1970. “In Defense of Eliminative Materialism”, Review of Metaphysics 24.
Rosen, G. 1990. “Modal Fictionalism”, Mind 99.
Rosen, G. 1993. “A Problem for Fictionalism About Possible Worlds”, Analysis 53.
Rosen, G. 1995. “Modal Fictionalism Fixed”, Analysis 55.
Ross, G. M. 1984. Leibniz. Oxford: Oxford University Press.
Rosser, J. B. 1936. “Extensions of Some Theorems of Gödel and Church”, Journal of
Symbolic Logic 1.
Rosser, J. B. 1939a. “On the Consistency of Quine’s New Foundations for Mathemati-
cal Logic”, Journal of Symbolic Logic 4.
Rosser, J. B. 1939b. “Definition by Induction in Quine’s New Foundations for Math-
ematical Logic”, Journal of Symbolic Logic 4.
Rosser, J. B. 1952. “The Axiom of Infinity in Quine’s New Foundations”, Journal of
Symbolic Logic 18.
Rothbart, D. 1976. “Propositions and Quine’s Indeterminacy of Radical Translation”,
Dialogue 18.
Rousseau, J. J. 1982. The Reveries of the Solitary Walker, C. Butterworth (trans.). New
York: Harper & Row.
Rowe, W. L. (ed.) 2001. God and the Problem of Evil. Oxford: Basil Blackwell.
Russell, B. 1905. “On Denoting”, Mind 14.
Russell, B. 1910–11. “Knowledge by Acquaintance and Knowledge by Description”,
Proceedings of the Aristotelian Society 11.
Russell, B. 1911–12. “On the Relations of Universals and Particulars”, Proceedings of
the Aristotelian Society 12.
Russell, B. 1957. Why I Am Not a Christian and Other Essays on Related Subjects,
edited with an appendix on the “Bertrand Russell Case” by P. Edwards. New York:
Simon and Schuster.
Russell, B. 1990. The Problems of Philosophy. Indianapolis, IN: Hackett.
Ryle, G. 1949. The Concept of Mind. New York: Barnes & Noble.
Ryser, H. J. 1963. Combinatorial Analysis. New York: Wiley.
Sacks, M. 1989. The World We Found: The Limits of Ontological Talk. London:
Duckworth.
Salmon, N. 1996. “Trans-World Identification and Stipulation”, Philosophical Studies 84.
Salmon, W. C. (ed.) 1970. Zeno’s Paradoxes. Indianapolis, IN: The Bobbs-Merrill
Company.
Sartre, J.-P. 1957. The Transcendence of the Ego: An Existentialist Theory of Conscious-
ness, translated and annotated with an introduction by F. Williams and R.
Kirkpatrick. New York: Farrar, Straus and Giroux. Originally published 1937.
Sartre, J.-P. 1992. Being and Nothingness: A Phenomenological Essay on Ontology,
translated with an introduction by H. Barnes. New York: Washington Square Press.
Scaltsas, T. 1989. “The Logic of the Dilemma of Participation and of the Third Man
Argument”, Apeiron 22.
Scaltsas, T. 1992. “A Necessary Falsehood in the Third Man Argument”, Phronesis 37.
Schlesinger, G. 1983. “Reconstructing McTaggart’s Argument”, Philosophy 58.
Schopenhauer, A. 1891. Arthur Schopenhauers Samtliche Werke [6 volumes], Julius
Frauenstädt (ed.). Wiesbaden: E. Brockhaus.
Schopenhauer, A. 1969. The World as Will and Representation [2 volumes], E. F. J.
Payne (trans.). New York: Dover.
Schopenhauer, A. 1974. On the Fourfold Root of the